Finite Group Databasebeta

← C139×#14725 #48009321

Subgroups — C139×#14725 #48009321

Order 35584.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C139C211yesmaximal, characteristic
2C23×C22⋊C4×C139C211yesmaximal, characteristic, complemented
3C2×#394×C139C212yesmaximal, complemented
4C2×#386×C139C211yesmaximal, characteristic, complemented
5C2×#386×C139C211yesmaximal, characteristic, complemented
6C2×#380×C139C211yesmaximal, characteristic, complemented
7C2×#379×C139C211yesmaximal, characteristic, complemented
8#1440×C139C212yesmaximal, complemented
9#1439×C139C212yesmaximal, complemented
10#1438×C139C212yesmaximal, complemented
11C22⋊#95×C139C211yesmaximal, characteristic, complemented
12C26×C139C2211yescharacteristic
13C23×D4×C139C2211yescharacteristic
14C23×D4×C139C2212yes—
15C24×C4×C139C2211yescharacteristic
16C24×C4×C139C2211yescharacteristic
17C2×#120×C139—24no—
18C2×#120×C139—24no—
19C2×#120×C139—24no—
20C22×C4⋊C4×C139C2212yescomplemented
21C22×C22⋊C4×C139—24no—
22C22×C22⋊C4×C139—28no—
23C22×C22⋊C4×C139C2211yescharacteristic
24C22×C22⋊C4×C139C2211yescharacteristic
25C22×C22⋊C4×C139C2212yes—
26C22×C22⋊C4×C139C2212yes—
27C22×C22⋊C4×C139C2212yes—
28C22×C22⋊C4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2212yes—
30C22×C22⋊C4×C139C2212yes—
31C22×C22⋊C4×C139C2211yescharacteristic, complemented
32C22×C22⋊C4×C139C2212yescomplemented
33C22×C22⋊C4×C139C2211yescharacteristic, complemented
34#394×C139—28no—
35#386×C139—24no—
36#386×C139—24no—
37#380×C139—24no—
38#379×C139—24no—
39C2×#95×C139C2212yescomplemented
40C2×#95×C139C2211yescharacteristic, complemented
41C2×#95×C139C2212yescomplemented
42C2×#95×C139C2211yescharacteristic, complemented
43C2×#95×C139C2212yescomplemented
44C2×#95×C139C2212yescomplemented
45C25×C139—24no—
46C25×C139—22no—
47C25×C139—24no—
48C25×C139—22no—
49C25×C139—22no—
50C25×C139—22no—
51C25×C139—22no—
52C25×C139—22no—
53C25×C139—42no—
54C25×C139—42no—
55C25×C139D414yes—
56C25×C139C2311yescharacteristic
57C25×C139C2312yes—
58C25×C139C2311yescharacteristic
59C22×D4×C139—24no—
60C22×D4×C139—24no—
61C22×D4×C139—22no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—24no—
68C22×D4×C139—24no—
69C22×D4×C139—24no—
70C22×D4×C139—42no—
71C22×D4×C139—42no—
72C22×D4×C139D414yes—
73C23×C4×C139—22no—
74C23×C4×C139—22no—
75C23×C4×C139—22no—
76C23×C4×C139—24no—
77C23×C4×C139—24no—
78C23×C4×C139—22no—
79C23×C4×C139—22no—
80C23×C4×C139—42no—
81C23×C4×C139—42no—
82C23×C4×C139D414yescomplemented
83C23×C4×C139C2312yes—
84C23×C4×C139C2311yescharacteristic
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2312yes—
88C23×C4×C139C2312yes—
89C23×C4×C139C2311yescharacteristic
90C23×C4×C139C2311yescharacteristic
91#120×C139—232no—
92C2×C4⋊C4×C139—24no—
93C2×C4⋊C4×C139—24no—
94C2×C4⋊C4×C139—42no—
95C2×C22⋊C4×C139—232no—
96C2×C22⋊C4×C139—24no—
97C2×C22⋊C4×C139—24no—
98C2×C22⋊C4×C139—22no—
99C2×C22⋊C4×C139—22no—
100C2×C22⋊C4×C139—24no—
101C2×C22⋊C4×C139—24no—
102C2×C22⋊C4×C139—24no—
103C2×C22⋊C4×C139—24no—
104C2×C22⋊C4×C139—24no—
105C2×C22⋊C4×C139—24no—
106C2×C22⋊C4×C139—24no—
107C2×C22⋊C4×C139—22no—
108C2×C22⋊C4×C139—24no—
109C2×C22⋊C4×C139—22no—
110C2×C22⋊C4×C139—22no—
111C2×C22⋊C4×C139—22no—
112C2×C22⋊C4×C139—22no—
113C2×C22⋊C4×C139—24no—
114C2×C22⋊C4×C139—24no—
115C2×C22⋊C4×C139—24no—
116C2×C22⋊C4×C139—22no—
117C2×C22⋊C4×C139—22no—
118C2×C22⋊C4×C139—22no—
119C2×C22⋊C4×C139—24no—
120C2×C22⋊C4×C139—24no—
121C2×C22⋊C4×C139—42no—
122C2×C22⋊C4×C139—42no—
123C2×C22⋊C4×C139—42no—
124C2×C22⋊C4×C139—42no—
125C2×C22⋊C4×C139D414yes—
126C2×C22⋊C4×C139D418yescomplemented
127#95×C139—24no—
128#95×C139—22no—
129#95×C139—22no—
130#95×C139—24no—
131#95×C139—24no—
132#95×C139—42no—
133C24×C139—22no—
134C24×C139—22no—
135C24×C139—22no—
136C24×C139—22no—
137C24×C139—28no—
138C24×C139—28no—
139C24×C139—216no—
140C24×C139—216no—
141C24×C139—28no—
142C24×C139—22no—
143C24×C139—22no—
144C24×C139—22no—
145C24×C139—22no—
146C24×C139—22no—
147C24×C139—22no—
148C24×C139—22no—
149C24×C139—22no—
150C24×C139—22no—
151C24×C139—22no—
152C24×C139—22no—
153C24×C139—22no—
154C24×C139—28no—
155C24×C139—28no—
156C24×C139—21no—
157C24×C139—22no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—22no—
164C24×C139—22no—
165C24×C139—22no—
166C24×C139—48no—
167C24×C139—48no—
168C24×C139—48no—
169C24×C139—48no—
170C24×C139—48no—
171C24×C139—48no—
172C24×C139—48no—
173C24×C139—48no—
174C24×C139—48no—
175C24×C139—44no—
176C24×C139—44no—
177C24×C139—48no—
178C24×C139—44no—
179C24×C139—44no—
180C24×C139—44no—
181C24×C139—44no—
182C24×C139C2×D412yes—
183C24×C139C2×D414yes—
184C24×C139C2×D414yes—
185C24×C139C2×D412yes—
186C24×C139C2×D412yes—
187C24×C139C2×D412yes—
188C24×C139C2×D412yes—
189C24×C139#4114yes—
190C24×C139#4112yes—
191C24×C139#4112yes—
192C24×C139#4112yes—
193C24×C139C2411yescharacteristic
194C2×D4×C139—216no—
195C2×D4×C139—28no—
196C2×D4×C139—28no—
197C2×D4×C139—28no—
198C2×D4×C139—48no—
199C2×D4×C139—48no—
200C2×D4×C139—48no—
201C2×D4×C139—48no—
202C2×D4×C139—48no—
203C2×D4×C139—48no—
204C2×D4×C139—44no—
205C2×D4×C139—44no—
206C2×D4×C139—44no—
207C2×D4×C139—44no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—22no—
211C22×C4×C139—28no—
212C22×C4×C139—28no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—22no—
216C22×C4×C139—22no—
217C22×C4×C139—22no—
218C22×C4×C139—22no—
219C22×C4×C139—22no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—22no—
223C22×C4×C139—22no—
224C22×C4×C139—21no—
225C22×C4×C139—22no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
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—28no—
236C22×C4×C139—21no—
237C22×C4×C139—22no—
238C22×C4×C139—22no—
239C22×C4×C139—21no—
240C22×C4×C139—22no—
241C22×C4×C139—22no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—22no—
245C22×C4×C139—21no—
246C22×C4×C139—22no—
247C22×C4×C139—21no—
248C22×C4×C139—22no—
249C22×C4×C139—22no—
250C22×C4×C139—22no—
251C22×C4×C139—22no—
252C22×C4×C139—22no—
253C22×C4×C139—44no—
254C22×C4×C139—48no—
255C22×C4×C139—48no—
256C22×C4×C139—48no—
257C22×C4×C139—48no—
258C22×C4×C139—44no—
259C22×C4×C139—44no—
260C22×C4×C139C2×D412yes—
261C22×C4×C139C2×D412yes—
262C22×C4×C139C2×D414yes—
263C22×C4×C139C2×D414yes—
264C22×C4×C139C2×D412yes—
265C22×C4×C139C2×D414yes—
266C4⋊C4×C139—48no—
267C22⋊C4×C139—216no—
268C22⋊C4×C139—216no—
269C22⋊C4×C139—28no—
270C22⋊C4×C139—216no—
271C22⋊C4×C139—48no—
272C22⋊C4×C139—44no—
273C22⋊C4×C139—48no—
274C22⋊C4×C139—44no—
275C22⋊C4×C139—48no—
276C22⋊C4×C139—44no—
277C22⋊C4×C139—44no—
278C23×C139—22no—
279C23×C139—24no—
280C23×C139—22no—
281C23×C139—24no—
282C23×C139—22no—
283C23×C139—24no—
284C23×C139—22no—
285C23×C139—24no—
286C23×C139—24no—
287C23×C139—24no—
288C23×C139—24no—
289C23×C139—24no—
290C23×C139—24no—
291C23×C139—24no—
292C23×C139—24no—
293C23×C139—24no—
294C23×C139—232no—
295C23×C139—24no—
296C23×C139—24no—
297C23×C139—24no—
298C23×C139—24no—
299C23×C139—24no—
300C23×C139—24no—
301C23×C139—24no—
302C23×C139—24no—
303C23×C139—24no—
304C23×C139—24no—
305C23×C139—24no—
306C23×C139—24no—
307C23×C139—24no—
308C23×C139—24no—
309C23×C139—24no—
310C23×C139—24no—
311C23×C139—24no—
312C23×C139—24no—
313C23×C139—22no—
314C23×C139—22no—
315C23×C139—22no—
316C23×C139—24no—
317C23×C139—24no—
318C23×C139—432no—
319C23×C139—432no—
320C23×C139—416no—
321C23×C139—416no—
322C23×C139—416no—
323C23×C139—416no—
324C23×C139—432no—
325C23×C139—432no—
326C23×C139—416no—
327C23×C139—42no—
328C23×C139—42no—
329C23×C139—42no—
330C23×C139—42no—
331C23×C139—42no—
332C23×C139—42no—
333C23×C139—42no—
334C23×C139—42no—
335C23×C139—42no—
336C23×C139—42no—
337C23×C139—42no—
338C23×C139—42no—
339C23×C139—42no—
340C23×C139—42no—
341C23×C139—42no—
342C23×C139—42no—
343C23×C139—416no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—42no—
348C23×C139—41no—
349C23×C139—42no—
350C23×C139—41no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—42no—
354C23×C139—41no—
355C23×C139—42no—
356C23×C139—42no—
357C23×C139—42no—
358C23×C139—42no—
359C23×C139—42no—
360C23×C139—42no—
361C23×C139—42no—
362C23×C139#12014yes—
363C23×C139#12118yes—
364C23×C139#12114yes—
365C23×C139#12114yes—
366C23×C139#12114yes—
367C23×C139#12314yes—
368C23×C139#12314yes—
369C23×C139#12414yes—
370C23×C139C22×D411yescharacteristic
371C23×C139C22×D411yescharacteristic
372C23×C139C22×D411yescharacteristic
373C23×C139C22×D412yes—
374C23×C139C22×D411yescharacteristic
375C23×C139C2×#4111yescharacteristic
376C23×C139C2×#4111yescharacteristic
377C23×C139C2×#4111yescharacteristic
378C23×C139C2×#4112yes—
379C23×C139H(5,𝔽2)12yes—
380C23×C139H(5,𝔽2)12yes—
381D4×C139—432no—
382D4×C139—416no—
383C2×C4×C139—22no—
384C2×C4×C139—22no—
385C2×C4×C139—24no—
386C2×C4×C139—24no—
387C2×C4×C139—24no—
388C2×C4×C139—22no—
389C2×C4×C139—22no—
390C2×C4×C139—24no—
391C2×C4×C139—22no—
392C2×C4×C139—22no—
393C2×C4×C139—22no—
394C2×C4×C139—22no—
395C2×C4×C139—24no—
396C2×C4×C139—24no—
397C2×C4×C139—24no—
398C2×C4×C139—24no—
399C2×C4×C139—416no—
400C2×C4×C139—416no—
401C2×C4×C139—42no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—42no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—42no—
408C2×C4×C139—42no—
409C2×C4×C139—42no—
410C2×C4×C139—42no—
411C2×C4×C139—42no—
412C2×C4×C139—42no—
413C2×C4×C139—42no—
414C2×C4×C139—42no—
415C2×C4×C139—41no—
416C2×C4×C139—42no—
417C2×C4×C139—41no—
418C2×C4×C139—42no—
419C2×C4×C139—41no—
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—41no—
427C2×C4×C139—42no—
428C2×C4×C139—42no—
429C2×C4×C139—42no—
430C2×C4×C139—42no—
431C2×C4×C139—42no—
432C2×C4×C139#12014yescomplemented
433C22×C139—24no—
434C22×C139—24no—
435C22×C139—24no—
436C22×C139—24no—
437C22×C139—28no—
438C22×C139—24no—
439C22×C139—28no—
440C22×C139—28no—
441C22×C139—28no—
442C22×C139—24no—
443C22×C139—28no—
444C22×C139—28no—
445C22×C139—28no—
446C22×C139—464no—
447C22×C139—44no—
448C22×C139—44no—
449C22×C139—44no—
450C22×C139—44no—
451C22×C139—44no—
452C22×C139—44no—
453C22×C139—44no—
454C22×C139—44no—
455C22×C139—44no—
456C22×C139—44no—
457C22×C139—44no—
458C22×C139—44no—
459C22×C139—42no—
460C22×C139—42no—
461C22×C139—44no—
462C22×C139—44no—
463C22×C139—42no—
464C22×C139—81no—
465C22×C139—81no—
466C22×C139—81no—
467C22×C139—81no—
468C22×C139—82no—
469C22×C139—82no—
470C22×C139#39418yescomplemented
471C22×C139C2×#12011yescharacteristic
472C22×C139C2×#12011yescharacteristic
473C22×C139C2×#12111yescharacteristic
474C22×C139C2×#12112yes—
475C22×C139C2×#12111yescharacteristic
476C22×C139C2×#12111yescharacteristic
477C22×C139C2×#12311yescharacteristic
478C22×C139C2×#12311yescharacteristic
479C22×C139#52511yescharacteristic
480C22×C139#52512yes—
481C22×C139C2×#12411yescharacteristic
482C22×C139#53412yes—
483C22×C139#53411yescharacteristic
484C22×C139#53511yescharacteristic
485C22×C139#53812yes—
486C22×C139D4212yes—
487C22×C139D4212yes—
488C22×C139#54612yes—
489C22×C139#54612yes—
490C22×C139#54612yes—
491C22×C139#54612yes—
492C22×C139#55112yes—
493C22×C139#55112yes—
494C4×C139—24no—
495C4×C139—42no—
496C4×C139—44no—
497C4×C139—42no—
498C4×C139—44no—
499C4×C139—81no—
500C4×C139—81no—
501C4×C139—82no—
502C2×C139—28no—
503C2×C139—48no—
504C2×C139—82no—
505C2×C139C2×#39411yescharacteristic
506C2×C139#240811yescharacteristic
507C2×C139#241011yescharacteristic
508C2×C139#241012yes—
509C2×C139#241111yescharacteristic
510C2×C139#241212yes—
511C2×C139#241812yes—
512C2×C139#247212yes—
513C2×C139#253411yescharacteristic
514C2×C139#261711yescharacteristic
515C2×C139#284711yescharacteristic
516#14725C13911yesmaximal, characteristic, direct product factor, Sylow
517C139#1472511yescharacteristic, direct product factor, Sylow
518C22×#120C2×C13911yescharacteristic
519C23×C22⋊C4C2×C13911yescharacteristic, complemented
520C2×#394C2×C13912yescomplemented
521C2×#386C2×C13911yescharacteristic, complemented
522C2×#386C2×C13911yescharacteristic, complemented
523C2×#380C2×C13911yescharacteristic, complemented
524C2×#379C2×C13911yescharacteristic, complemented
525#1440C2×C13912yescomplemented
526#1439C2×C13912yescomplemented
527#1438C2×C13912yescomplemented
528C22⋊#95C2×C13911yescharacteristic, complemented
529C26C22×C13911yescharacteristic
530C23×D4C22×C13911yescharacteristic
531C23×D4C22×C13912yes—
532C24×C4C22×C13911yescharacteristic
533C24×C4C22×C13911yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C13912yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C13912yes—
541C22×C22⋊C4C22×C13912yes—
542C22×C22⋊C4C22×C13912yes—
543C22×C22⋊C4C22×C13911yescharacteristic
544C22×C22⋊C4C22×C13911yescharacteristic
545C22×C22⋊C4C22×C13911yescharacteristic
546C22×C22⋊C4C22×C13912yes—
547C22×C22⋊C4C22×C13912yes—
548C22×C22⋊C4C22×C13911yescharacteristic, complemented
549C22×C22⋊C4C22×C13912yescomplemented
550C22×C22⋊C4C22×C13911yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C13912yescomplemented
557C2×#95C22×C13912yescomplemented
558C2×#95C22×C13911yescharacteristic, complemented
559C2×#95C22×C13912yescomplemented
560C2×#95C22×C13911yescharacteristic, complemented
561C2×#95C22×C13912yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C13914yes—
573C25C23×C13911yescharacteristic
574C25C23×C13912yes—
575C25C23×C13911yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C13914yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C13914yescomplemented
600C23×C4C23×C13912yes—
601C23×C4C23×C13911yescharacteristic
602C23×C4C23×C13911yescharacteristic
603C23×C4C23×C13911yescharacteristic
604C23×C4C23×C13912yes—
605C23×C4C23×C13912yes—
606C23×C4C23×C13911yescharacteristic
607C23×C4C23×C13911yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C13914yes—
643C2×C22⋊C4D4×C13918yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C13912yes—
700C24C2×D4×C13914yes—
701C24C2×D4×C13914yes—
702C24C2×D4×C13912yes—
703C24C2×D4×C13912yes—
704C24C2×D4×C13912yes—
705C24C2×D4×C13912yes—
706C24#41×C13914yes—
707C24#41×C13912yes—
708C24#41×C13912yes—
709C24#41×C13912yes—
710C24C24×C13911yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C13912yes—
778C22×C4C2×D4×C13912yes—
779C22×C4C2×D4×C13914yes—
780C22×C4C2×D4×C13914yes—
781C22×C4C2×D4×C13912yes—
782C22×C4C2×D4×C13914yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C13914yes—
880C23#121×C13918yes—
881C23#121×C13914yes—
882C23#121×C13914yes—
883C23#121×C13914yes—
884C23#123×C13914yes—
885C23#123×C13914yes—
886C23#124×C13914yes—
887C23C22×D4×C13911yescharacteristic
888C23C22×D4×C13911yescharacteristic
889C23C22×D4×C13911yescharacteristic
890C23C22×D4×C13912yes—
891C23C22×D4×C13911yescharacteristic
892C23C2×#41×C13911yescharacteristic
893C23C2×#41×C13911yescharacteristic
894C23C2×#41×C13911yescharacteristic
895C23C2×#41×C13912yes—
896C23H(5,𝔽2)×C13912yes—
897C23H(5,𝔽2)×C13912yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C13914yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C13918yescomplemented
988C22C2×#120×C13911yescharacteristic
989C22C2×#120×C13911yescharacteristic
990C22C2×#121×C13911yescharacteristic
991C22C2×#121×C13911yescharacteristic
992C22C2×#121×C13912yes—
993C22C2×#121×C13911yescharacteristic
994C22C2×#123×C13911yescharacteristic
995C22C2×#123×C13911yescharacteristic
996C22#525×C13911yescharacteristic
997C22#525×C13912yes—
998C22C2×#124×C13911yescharacteristic
999C22#534×C13911yescharacteristic
1000C22#534×C13912yes—
1001C22#535×C13911yescharacteristic
1002C22#538×C13912yes—
1003C22D42×C13912yes—
1004C22D42×C13912yes—
1005C22#546×C13912yes—
1006C22#546×C13912yes—
1007C22#546×C13912yes—
1008C22#546×C13912yes—
1009C22#551×C13912yes—
1010C22#551×C13912yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C13911yescharacteristic
1023C2#2408×C13911yescharacteristic
1024C2#2410×C13911yescharacteristic
1025C2#2410×C13912yes—
1026C2#2411×C13911yescharacteristic
1027C2#2412×C13912yes—
1028C2#2418×C13912yes—
1029C2#2472×C13912yes—
1030C2#2534×C13911yescharacteristic
1031C2#2617×C13911yescharacteristic
1032C2#2847×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC22×#120×C139C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C139C2semidirect
3. C2×#394×C139C2semidirect
4. C2×#386×C139C2semidirect
5. C2×#386×C139C2semidirect
6. C2×#380×C139C2semidirect
7. C2×#379×C139C2semidirect
8. #1440×C139C2semidirect
9. #1439×C139C2semidirect
10. #1438×C139C2semidirect
11. C22⋊#95×C139C2semidirect
20. C22×C4⋊C4×C139C22semidirect
31. C22×C22⋊C4×C139C22semidirect
32. C22×C22⋊C4×C139C22semidirect
33. C22×C22⋊C4×C139C22semidirect
39. C2×#95×C139C22semidirect
40. C2×#95×C139C22semidirect
41. C2×#95×C139C22semidirect
42. C2×#95×C139C22semidirect
43. C2×#95×C139C22semidirect
44. C2×#95×C139C22semidirect
82. C23×C4×C139D4semidirect
126. C2×C22⋊C4×C139D4semidirect
432. C2×C4×C139#120semidirect
470. C22×C139#394semidirect
516. #14725C139direct (N × H)
517. C139#14725direct (N × H)
519. C23×C22⋊C4C2×C139semidirect
520. C2×#394C2×C139semidirect
521. C2×#386C2×C139semidirect
522. C2×#386C2×C139semidirect
523. C2×#380C2×C139semidirect
524. C2×#379C2×C139semidirect
525. #1440C2×C139semidirect
526. #1439C2×C139semidirect
527. #1438C2×C139semidirect
528. C22⋊#95C2×C139semidirect
537. C22×C4⋊C4C22×C139semidirect
548. C22×C22⋊C4C22×C139semidirect
549. C22×C22⋊C4C22×C139semidirect
550. C22×C22⋊C4C22×C139semidirect
556. C2×#95C22×C139semidirect
557. C2×#95C22×C139semidirect
558. C2×#95C22×C139semidirect
559. C2×#95C22×C139semidirect
560. C2×#95C22×C139semidirect
561. C2×#95C22×C139semidirect
599. C23×C4D4×C139semidirect
643. C2×C22⋊C4D4×C139semidirect
949. C2×C4#120×C139semidirect
987. C22#394×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1392
C23×C22⋊C4×C1392
C2×#394×C1392
C2×#386×C1392
C2×#380×C1392
C2×#379×C1392
#1440×C1392
#1439×C1392
#1438×C1392
C22⋊#95×C1392
#14725139