Finite Group Databasebeta

← C139×#24405 #48019001

Subgroups — C139×#24405 #48019001

Order 35584.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C139C211yesmaximal, characteristic
2C2×#458×C139C211yesmaximal, characteristic, complemented
3C22×#99×C139C211yesmaximal, characteristic, complemented
4#2412×C139C212yesmaximal, complemented
5#2405×C139C211yesmaximal, characteristic, complemented
6#2044×C139C212yesmaximal, complemented
7#2022×C139C212yesmaximal, complemented
8#1898×C139C212yesmaximal, complemented
9#1890×C139C211yesmaximal, characteristic, complemented
10#1867×C139C211yesmaximal, characteristic, complemented
11#1790×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic
13C23×D4×C139C2211yescharacteristic
14#546×C139—22no—
15#546×C139—22no—
16D42×C139—22no—
17D42×C139—22no—
18#535×C139—21no—
19#534×C139—21no—
20#534×C139C2212yes—
21#525×C139—21no—
22C2×#123×C139C2211yescharacteristic
23C2×#123×C139C2212yescomplemented
24C2×#123×C139C2211yescharacteristic, complemented
25C2×#120×C139—21no—
26C2×#120×C139C2212yes—
27#518×C139C2211yescharacteristic
28C22×C22⋊C4×C139C2211yescharacteristic, complemented
29C22×C22⋊C4×C139C2212yescomplemented
30#458×C139—24no—
31C2×#99×C139—24no—
32C2×#99×C139C2211yescharacteristic
33C2×#99×C139C2211yescharacteristic
34C2×#99×C139C2212yescomplemented
35C2×#99×C139C2212yescomplemented
36C2×#99×C139C2212yescomplemented
37#397×C139—22no—
38#394×C139—21no—
39#394×C139—21no—
40#394×C139—22no—
41#386×C139—22no—
42#386×C139C2211yescharacteristic
43#386×C139C2211yescharacteristic, complemented
44#386×C139C2212yescomplemented
45#385×C139—21no—
46#385×C139C2212yescomplemented
47#381×C139C2212yescomplemented
48#380×C139—22no—
49#379×C139—21no—
50#379×C139C2211yescharacteristic, complemented
51#342×C139C2212yescomplemented
52#342×C139C2212yescomplemented
53C25×C139D411yescharacteristic
54C25×C139C2311yescharacteristic
55H(5,𝔽2)×C139—22no—
56H(5,𝔽2)×C139—22no—
57H(5,𝔽2)×C139—42no—
58C2×#41×C139—21no—
59C2×#41×C139—22no—
60C22×D4×C139—21no—
61C22×D4×C139—22no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—42no—
69C22×D4×C139D411yescharacteristic
70C22×D4×C139D411yescharacteristic
71C22×D4×C139D412yes—
72C22×D4×C139D412yes—
73C22×D4×C139C2312yes—
74C22×D4×C139C2311yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C23×C4×C139—22no—
77C23×C4×C139D411yescharacteristic
78C23×C4×C139C2311yescharacteristic
79C23×C4×C139C2311yescharacteristic
80#127×C139—22no—
81#124×C139—22no—
82#123×C139—22no—
83#123×C139—22no—
84#123×C139—22no—
85#123×C139—22no—
86#123×C139—22no—
87#123×C139—24no—
88#123×C139—42no—
89#123×C139—42no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—22no—
95#121×C139—22no—
96#121×C139—22no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#120×C139—22no—
101#120×C139—22no—
102#120×C139—22no—
103#120×C139—22no—
104#120×C139—22no—
105#120×C139—22no—
106#120×C139—22no—
107#120×C139—22no—
108#120×C139—22no—
109C4×D4×C139—22no—
110C4×D4×C139—22no—
111C4×D4×C139—22no—
112C4×D4×C139—22no—
113#117×C139—21no—
114C2×C4⋊C4×C139—22no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139—22no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—24no—
122C2×C22⋊C4×C139—22no—
123C2×C22⋊C4×C139—22no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—22no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—22no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—22no—
135C2×C22⋊C4×C139—42no—
136C2×C22⋊C4×C139D412yes—
137C2×C22⋊C4×C139D412yes—
138C2×C22⋊C4×C139C2312yes—
139C2×C22⋊C4×C139C2311yescharacteristic
140C2×C22⋊C4×C139C2311yescharacteristic
141C2×C22⋊C4×C139C2312yes—
142C2×C22⋊C4×C139C2312yes—
143#99×C139—22no—
144#99×C139—24no—
145#99×C139—24no—
146#99×C139—42no—
147#99×C139D414yescomplemented
148#95×C139—22no—
149#95×C139—22no—
150#95×C139—22no—
151#95×C139—22no—
152#95×C139—21no—
153#95×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139—22no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—22no—
161C24×C139—41no—
162C24×C139—42no—
163C24×C139—42no—
164C24×C139—81no—
165C24×C139—81no—
166C24×C139C2×D411yescharacteristic
167C24×C139C2×D412yes—
168C24×C139C2×D411yescharacteristic
169C24×C139C2×D412yes—
170C24×C139C2×D412yes—
171C24×C139C2×D411yescharacteristic
172C24×C139C2×D411yescharacteristic
173C24×C139C2411yescharacteristic
174#41×C139—44no—
175#41×C139—44no—
176#41×C139—42no—
177#41×C139—42no—
178C2×Q8×C139—21no—
179C2×D4×C139—22no—
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—21no—
183C2×D4×C139—22no—
184C2×D4×C139—22no—
185C2×D4×C139—22no—
186C2×D4×C139—22no—
187C2×D4×C139—22no—
188C2×D4×C139—21no—
189C2×D4×C139—22no—
190C2×D4×C139—22no—
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—21no—
194C2×D4×C139—22no—
195C2×D4×C139—22no—
196C2×D4×C139—22no—
197C2×D4×C139—22no—
198C2×D4×C139—22no—
199C2×D4×C139—22no—
200C2×D4×C139—22no—
201C2×D4×C139—22no—
202C2×D4×C139—22no—
203C2×D4×C139—41no—
204C2×D4×C139—41no—
205C2×D4×C139—44no—
206C2×D4×C139—44no—
207C2×D4×C139—44no—
208C2×D4×C139—44no—
209C2×D4×C139—44no—
210C2×D4×C139—44no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—44no—
214C2×D4×C139—82no—
215C2×D4×C139—82no—
216C2×D4×C139—82no—
217C2×D4×C139C2×D412yes—
218C2×D4×C139#4112yes—
219C22×C4×C139—21no—
220C22×C4×C139—22no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—22no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—22no—
227C22×C4×C139—22no—
228C22×C4×C139—21no—
229C22×C4×C139—22no—
230C22×C4×C139—22no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—22no—
237C22×C4×C139—41no—
238C22×C4×C139—44no—
239C22×C4×C139—44no—
240C22×C4×C139—81no—
241C22×C4×C139—82no—
242C22×C4×C139C2×D412yes—
243C22×C4×C139C2×D411yescharacteristic
244C22×C4×C139C2×D411yescharacteristic
245C22×C4×C139C2×D412yes—
246C22×C4×C139C2×D412yes—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—22no—
250C4⋊C4×C139—22no—
251C4⋊C4×C139—44no—
252C4⋊C4×C139—42no—
253C4⋊C4×C139—42no—
254C4⋊C4×C139—82no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—22no—
257C22⋊C4×C139—22no—
258C22⋊C4×C139—22no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—22no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—22no—
264C22⋊C4×C139—22no—
265C22⋊C4×C139—22no—
266C22⋊C4×C139—22no—
267C22⋊C4×C139—22no—
268C22⋊C4×C139—21no—
269C22⋊C4×C139—21no—
270C22⋊C4×C139—22no—
271C22⋊C4×C139—22no—
272C22⋊C4×C139—44no—
273C22⋊C4×C139—44no—
274C22⋊C4×C139—42no—
275C22⋊C4×C139—42no—
276C22⋊C4×C139—41no—
277C22⋊C4×C139—42no—
278C22⋊C4×C139—41no—
279C22⋊C4×C139—42no—
280C22⋊C4×C139—81no—
281C22⋊C4×C139—81no—
282C22⋊C4×C139—81no—
283C22⋊C4×C139—82no—
284C22⋊C4×C139C2×D414yescomplemented
285C42×C139—22no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—22no—
290C23×C139—22no—
291C23×C139—22no—
292C23×C139—24no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—22no—
297C23×C139—22no—
298C23×C139—21no—
299C23×C139—22no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—22no—
303C23×C139—22no—
304C23×C139—42no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—42no—
310C23×C139—42no—
311C23×C139—41no—
312C23×C139—42no—
313C23×C139—42no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—42no—
319C23×C139—42no—
320C23×C139—42no—
321C23×C139—42no—
322C23×C139—42no—
323C23×C139—81no—
324C23×C139—81no—
325C23×C139—82no—
326C23×C139—82no—
327C23×C139—84no—
328C23×C139—81no—
329C23×C139—81no—
330C23×C139—84no—
331C23×C139—84no—
332C23×C139#12011yescharacteristic
333C23×C139#12012yes—
334C23×C139#12011yescharacteristic
335C23×C139#12112yes—
336C23×C139C22×D411yescharacteristic
337C23×C139C22×D412yes—
338C23×C139C22×D411yescharacteristic
339C23×C139C2×#4111yescharacteristic
340C23×C139H(5,𝔽2)12yes—
341Q8×C139—42no—
342D4×C139—24no—
343D4×C139—24no—
344D4×C139—44no—
345D4×C139—42no—
346D4×C139—44no—
347D4×C139—44no—
348D4×C139—44no—
349D4×C139—42no—
350D4×C139—42no—
351D4×C139—42no—
352D4×C139—42no—
353D4×C139—42no—
354D4×C139—42no—
355D4×C139—44no—
356D4×C139—82no—
357D4×C139—82no—
358D4×C139—82no—
359D4×C139—82no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—22no—
363C2×C4×C139—22no—
364C2×C4×C139—22no—
365C2×C4×C139—21no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—24no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—42no—
372C2×C4×C139—42no—
373C2×C4×C139—44no—
374C2×C4×C139—42no—
375C2×C4×C139—42no—
376C2×C4×C139—42no—
377C2×C4×C139—42no—
378C2×C4×C139—42no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
382C2×C4×C139—41no—
383C2×C4×C139—42no—
384C2×C4×C139—42no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—42no—
388C2×C4×C139—42no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—42no—
396C2×C4×C139—42no—
397C2×C4×C139—42no—
398C2×C4×C139—81no—
399C2×C4×C139—81no—
400C2×C4×C139—88no—
401C2×C4×C139#12112yes—
402C22×C139—21no—
403C22×C139—22no—
404C22×C139—21no—
405C22×C139—22no—
406C22×C139—21no—
407C22×C139—21no—
408C22×C139—21no—
409C22×C139—22no—
410C22×C139—22no—
411C22×C139—22no—
412C22×C139—21no—
413C22×C139—21no—
414C22×C139—22no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—42no—
418C22×C139—44no—
419C22×C139—44no—
420C22×C139—42no—
421C22×C139—42no—
422C22×C139—42no—
423C22×C139—42no—
424C22×C139—41no—
425C22×C139—41no—
426C22×C139—42no—
427C22×C139—41no—
428C22×C139—42no—
429C22×C139—41no—
430C22×C139—42no—
431C22×C139—41no—
432C22×C139—82no—
433C22×C139—81no—
434C22×C139—81no—
435C22×C139—81no—
436C22×C139—82no—
437C22×C139—84no—
438C22×C139—82no—
439C22×C139—82no—
440C22×C139—81no—
441C22×C139—84no—
442C22×C139—162no—
443C22×C139#45812yescomplemented
444C22×C139C2×#12011yescharacteristic
445C22×C139C2×#12111yescharacteristic
446C22×C139#53411yescharacteristic
447C22×C139D4212yes—
448C22×C139#54612yes—
449C4×C139—22no—
450C4×C139—44no—
451C4×C139—41no—
452C4×C139—42no—
453C4×C139—42no—
454C4×C139—42no—
455C4×C139—81no—
456C4×C139—81no—
457C4×C139—82no—
458C4×C139—81no—
459C4×C139—81no—
460C2×C139—22no—
461C2×C139—21no—
462C2×C139—21no—
463C2×C139—22no—
464C2×C139—22no—
465C2×C139—42no—
466C2×C139—41no—
467C2×C139—42no—
468C2×C139—81no—
469C2×C139—82no—
470C2×C139#241011yescharacteristic
471C2×C139C2×#45811yescharacteristic
472C2×C139#302611yescharacteristic
473#24405C13911yesmaximal, characteristic, direct product factor, Sylow
474C139#2440511yescharacteristic, direct product factor, Sylow
475#3484C2×C13911yescharacteristic
476C2×#458C2×C13911yescharacteristic, complemented
477C22×#99C2×C13911yescharacteristic, complemented
478#2412C2×C13912yescomplemented
479#2405C2×C13911yescharacteristic, complemented
480#2044C2×C13912yescomplemented
481#2022C2×C13912yescomplemented
482#1898C2×C13912yescomplemented
483#1890C2×C13911yescharacteristic, complemented
484#1867C2×C13911yescharacteristic, complemented
485#1790C2×C13911yescharacteristic, complemented
486C2×H(5,𝔽2)C22×C13911yescharacteristic
487C23×D4C22×C13911yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C13912yes—
495#525—21no—
496C2×#123C22×C13911yescharacteristic
497C2×#123C22×C13912yescomplemented
498C2×#123C22×C13911yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C13912yes—
501#518C22×C13911yescharacteristic
502C22×C22⋊C4C22×C13911yescharacteristic, complemented
503C22×C22⋊C4C22×C13912yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C13911yescharacteristic
507C2×#99C22×C13911yescharacteristic
508C2×#99C22×C13912yescomplemented
509C2×#99C22×C13912yescomplemented
510C2×#99C22×C13912yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C13911yescharacteristic
517#386C22×C13911yescharacteristic, complemented
518#386C22×C13912yescomplemented
519#385—21no—
520#385C22×C13912yescomplemented
521#381C22×C13912yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C13911yescharacteristic, complemented
525#342C22×C13912yescomplemented
526#342C22×C13912yescomplemented
527C25D4×C13911yescharacteristic
528C25C23×C13911yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C13911yescharacteristic
544C22×D4D4×C13911yescharacteristic
545C22×D4D4×C13912yes—
546C22×D4D4×C13912yes—
547C22×D4C23×C13912yes—
548C22×D4C23×C13911yescharacteristic
549C22×D4C23×C13911yescharacteristic
550C23×C4—22no—
551C23×C4D4×C13911yescharacteristic
552C23×C4C23×C13911yescharacteristic
553C23×C4C23×C13911yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C13912yes—
611C2×C22⋊C4D4×C13912yes—
612C2×C22⋊C4C23×C13912yes—
613C2×C22⋊C4C23×C13911yescharacteristic
614C2×C22⋊C4C23×C13911yescharacteristic
615C2×C22⋊C4C23×C13912yes—
616C2×C22⋊C4C23×C13912yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C13914yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C13911yescharacteristic
641C24C2×D4×C13912yes—
642C24C2×D4×C13911yescharacteristic
643C24C2×D4×C13912yes—
644C24C2×D4×C13912yes—
645C24C2×D4×C13911yescharacteristic
646C24C2×D4×C13911yescharacteristic
647C24C24×C13911yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C13912yes—
692C2×D4#41×C13912yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C13912yes—
717C22×C4C2×D4×C13911yescharacteristic
718C22×C4C2×D4×C13911yescharacteristic
719C22×C4C2×D4×C13912yes—
720C22×C4C2×D4×C13912yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C13914yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C13911yescharacteristic
807C23#120×C13912yes—
808C23#120×C13911yescharacteristic
809C23#121×C13912yes—
810C23C22×D4×C13911yescharacteristic
811C23C22×D4×C13912yes—
812C23C22×D4×C13911yescharacteristic
813C23C2×#41×C13911yescharacteristic
814C23H(5,𝔽2)×C13912yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C13912yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C13912yescomplemented
918C22C2×#120×C13911yescharacteristic
919C22C2×#121×C13911yescharacteristic
920C22#534×C13911yescharacteristic
921C22D42×C13912yes—
922C22#546×C13912yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2410×C13911yescharacteristic
945C2C2×#458×C13911yescharacteristic
946C2#3026×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC24C24×C139
prime radical#3484×C139C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C139C2semidirect
3. C22×#99×C139C2semidirect
4. #2412×C139C2semidirect
5. #2405×C139C2semidirect
6. #2044×C139C2semidirect
7. #2022×C139C2semidirect
8. #1898×C139C2semidirect
9. #1890×C139C2semidirect
10. #1867×C139C2semidirect
11. #1790×C139C2semidirect
23. C2×#123×C139C22semidirect
24. C2×#123×C139C22semidirect
28. C22×C22⋊C4×C139C22semidirect
29. C22×C22⋊C4×C139C22semidirect
34. C2×#99×C139C22semidirect
35. C2×#99×C139C22semidirect
36. C2×#99×C139C22semidirect
43. #386×C139C22semidirect
44. #386×C139C22semidirect
46. #385×C139C22semidirect
47. #381×C139C22semidirect
50. #379×C139C22semidirect
51. #342×C139C22semidirect
52. #342×C139C22semidirect
147. #99×C139D4semidirect
284. C22⋊C4×C139C2×D4semidirect
443. C22×C139#458semidirect
473. #24405C139direct (N × H)
474. C139#24405direct (N × H)
476. C2×#458C2×C139semidirect
477. C22×#99C2×C139semidirect
478. #2412C2×C139semidirect
479. #2405C2×C139semidirect
480. #2044C2×C139semidirect
481. #2022C2×C139semidirect
482. #1898C2×C139semidirect
483. #1890C2×C139semidirect
484. #1867C2×C139semidirect
485. #1790C2×C139semidirect
497. C2×#123C22×C139semidirect
498. C2×#123C22×C139semidirect
502. C22×C22⋊C4C22×C139semidirect
503. C22×C22⋊C4C22×C139semidirect
508. C2×#99C22×C139semidirect
509. C2×#99C22×C139semidirect
510. C2×#99C22×C139semidirect
517. #386C22×C139semidirect
518. #386C22×C139semidirect
520. #385C22×C139semidirect
521. #381C22×C139semidirect
524. #379C22×C139semidirect
525. #342C22×C139semidirect
526. #342C22×C139semidirect
621. #99D4×C139semidirect
758. C22⋊C4C2×D4×C139semidirect
917. C22#458×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
C2×#458×C1392
C22×#99×C1392
#2412×C1392
#2405×C1392
#2044×C1392
#2022×C1392
#1898×C1392
#1890×C1392
#1867×C1392
#1790×C1392
#24405139