Finite Group Databasebeta

← C139×#24140 #48018736

Subgroups — C139×#24140 #48018736

Order 35584.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C139C211yesmaximal, characteristic, complemented
2#2848×C139C211yesmaximal, characteristic, complemented
3#2847×C139C211yesmaximal, characteristic, complemented
4C4×#120×C139C211yesmaximal, characteristic, complemented
5#2044×C139C212yesmaximal, complemented
6#2021×C139C212yesmaximal, complemented
7#1996×C139C211yesmaximal, characteristic, complemented
8#1964×C139C211yesmaximal, characteristic, complemented
9#1889×C139C212yesmaximal, complemented
10#1867×C139C212yesmaximal, complemented
11#1799×C139C211yesmaximal, characteristic, complemented
12C24×C4×C139C2211yescharacteristic
13#553×C139—21no—
14#553×C139—22no—
15#552×C139—21no—
16#551×C139—22no—
17#548×C139—21no—
18#546×C139—21no—
19#539×C139—21no—
20#538×C139—21no—
21#534×C139C2212yes—
22#529×C139—21no—
23#525×C139—21no—
24C2×C22⋊Q8×C139—21no—
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×#121×C139—21no—
27C2×#121×C139C2211yescharacteristic
28C2×#120×C139C2211yescharacteristic
29C2×#120×C139C2212yes—
30#518×C139C2212yes—
31C2×C4×D4×C139—21no—
32C2×C4×D4×C139C2211yescharacteristic
33C2×#99×C139C2212yes—
34C2×#99×C139C2212yes—
35C2×#99×C139C2212yes—
36#386×C139—21no—
37#386×C139—22no—
38#386×C139C2211yescharacteristic
39#386×C139C2212yes—
40#385×C139—21no—
41#385×C139—22no—
42#385×C139C2211yescharacteristic
43#385×C139C2212yes—
44#380×C139—21no—
45#380×C139—21no—
46#380×C139C2211yescharacteristic
47#380×C139C2211yescharacteristic
48#379×C139C2212yes—
49#379×C139C2211yescharacteristic
50C4×C22⋊C4×C139—21no—
51C4×C22⋊C4×C139C2211yescharacteristic
52#342×C139C2212yes—
53#342×C139C2212yes—
54#342×C139C2212yes—
55C25×C139C2311yescharacteristic
56C2×#41×C139—21no—
57C22×Q8×C139D411yescharacteristic, complemented
58C22×D4×C139—21no—
59C22×D4×C139—22no—
60C22×D4×C139D411yescharacteristic, complemented
61C22×D4×C139C2311yescharacteristic
62C22×D4×C139C2312yes—
63C23×C4×C139—21no—
64C23×C4×C139—21no—
65C23×C4×C139—21no—
66C23×C4×C139—21no—
67C23×C4×C139—21no—
68C23×C4×C139—21no—
69C23×C4×C139—44no—
70C23×C4×C139D411yescharacteristic, complemented
71C23×C4×C139C2311yescharacteristic
72C23×C4×C139C2311yescharacteristic
73#126×C139—22no—
74#126×C139—22no—
75#126×C139—22no—
76#125×C139—21no—
77#125×C139—22no—
78#124×C139—21no—
79#124×C139—22no—
80#123×C139—22no—
81#123×C139—22no—
82#123×C139—22no—
83#123×C139—22no—
84#123×C139—22no—
85C22⋊Q8×C139—21no—
86C22⋊Q8×C139—22no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—21no—
90C22⋊Q8×C139—21no—
91C22⋊Q8×C139—44no—
92#121×C139—21no—
93#121×C139—22no—
94#121×C139—21no—
95#121×C139—21no—
96#121×C139—21no—
97#121×C139—21no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—44no—
101#120×C139—22no—
102#120×C139—22no—
103#120×C139—22no—
104#120×C139—22no—
105#120×C139—24no—
106#120×C139—42no—
107C4×Q8×C139—21no—
108C4×D4×C139—22no—
109C4×D4×C139—21no—
110C4×D4×C139—21no—
111C4×D4×C139—21no—
112C4×D4×C139—21no—
113C4×D4×C139—21no—
114C4×D4×C139—22no—
115C4×D4×C139—22no—
116C4×D4×C139—22no—
117C4×D4×C139—22no—
118C4×D4×C139—44no—
119#117×C139—21no—
120#117×C139—22no—
121#117×C139—22no—
122C2×C4⋊C4×C139—21no—
123C2×C4⋊C4×C139—21no—
124C2×C4⋊C4×C139—21no—
125C2×C4⋊C4×C139—22no—
126C2×C4⋊C4×C139D411yescharacteristic, complemented
127C2×C4⋊C4×C139D411yescharacteristic, complemented
128C2×C4⋊C4×C139D411yescharacteristic, complemented
129C2×C4⋊C4×C139D412yescomplemented
130C2×C22⋊C4×C139—22no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—22no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—22no—
136C2×C22⋊C4×C139—22no—
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—22no—
139C2×C22⋊C4×C139D411yescharacteristic, complemented
140C2×C22⋊C4×C139D412yescomplemented
141C2×C22⋊C4×C139C2312yes—
142C2×C22⋊C4×C139C2311yescharacteristic
143C2×C22⋊C4×C139C2312yes—
144C2×C22⋊C4×C139C2311yescharacteristic
145C2×C22⋊C4×C139C2312yes—
146C2×C22⋊C4×C139C2311yescharacteristic
147C2×C42×C139—21no—
148C2×C42×C139D411yescharacteristic, complemented
149#99×C139—24no—
150#99×C139—42no—
151#99×C139—42no—
152#95×C139—21no—
153#95×C139—21no—
154#95×C139—21no—
155#95×C139—22no—
156#95×C139—22no—
157#95×C139—21no—
158#95×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—21no—
165C24×C139—42no—
166C24×C139—42no—
167C24×C139C2×D412yes—
168C24×C139C2×D411yescharacteristic
169C24×C139#4112yescomplemented
170C24×C139C2411yescharacteristic
171#41×C139—82no—
172C2×Q8×C139—21no—
173C2×Q8×C139—21no—
174C2×Q8×C139—42no—
175C2×D4×C139—24no—
176C2×D4×C139—21no—
177C2×D4×C139—22no—
178C2×D4×C139—21no—
179C2×D4×C139—22no—
180C2×D4×C139—22no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—22no—
184C2×D4×C139—21no—
185C2×D4×C139—22no—
186C2×D4×C139—21no—
187C2×D4×C139—22no—
188C2×D4×C139—22no—
189C2×D4×C139—22no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—44no—
196C2×D4×C139—44no—
197C2×D4×C139—44no—
198C22×C4×C139—24no—
199C22×C4×C139—24no—
200C22×C4×C139—24no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—22no—
206C22×C4×C139—22no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—22no—
211C22×C4×C139—22no—
212C22×C4×C139—42no—
213C22×C4×C139—42no—
214C22×C4×C139—42no—
215C22×C4×C139—42no—
216C22×C4×C139—42no—
217C22×C4×C139—42no—
218C22×C4×C139—42no—
219C22×C4×C139—42no—
220C22×C4×C139—42no—
221C22×C4×C139—42no—
222C22×C4×C139—42no—
223C22×C4×C139—42no—
224C22×C4×C139—41no—
225C22×C4×C139—41no—
226C22×C4×C139—41no—
227C22×C4×C139—41no—
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D412yes—
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D412yes—
235C22×C4×C139C2×D411yescharacteristic
236C22×C4×C139C2×D412yes—
237C22×C4×C139C2×D411yescharacteristic
238C22×C4×C139C2×D411yescharacteristic
239C22×C4×C139C2×D411yescharacteristic
240C4⋊C4×C139—22no—
241C4⋊C4×C139—22no—
242C4⋊C4×C139—22no—
243C4⋊C4×C139—22no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—22no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—22no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—42no—
253C4⋊C4×C139—42no—
254C4⋊C4×C139—42no—
255C4⋊C4×C139—44no—
256C22⋊C4×C139—22no—
257C22⋊C4×C139—22no—
258C22⋊C4×C139—24no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—22no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—21no—
264C22⋊C4×C139—22no—
265C22⋊C4×C139—21no—
266C22⋊C4×C139—22no—
267C22⋊C4×C139—21no—
268C22⋊C4×C139—22no—
269C22⋊C4×C139—21no—
270C22⋊C4×C139—21no—
271C22⋊C4×C139—22no—
272C22⋊C4×C139—22no—
273C22⋊C4×C139—22no—
274C22⋊C4×C139—21no—
275C22⋊C4×C139—22no—
276C22⋊C4×C139—22no—
277C22⋊C4×C139—21no—
278C22⋊C4×C139—44no—
279C22⋊C4×C139—42no—
280C22⋊C4×C139—44no—
281C22⋊C4×C139—44no—
282C22⋊C4×C139—42no—
283C22⋊C4×C139—42no—
284C22⋊C4×C139—44no—
285C22⋊C4×C139#4112yescomplemented
286C42×C139—22no—
287C42×C139—22no—
288C42×C139—21no—
289C42×C139—21no—
290C42×C139—42no—
291C23×C139—22no—
292C23×C139—22no—
293C23×C139—22no—
294C23×C139—22no—
295C23×C139—22no—
296C23×C139—22no—
297C23×C139—22no—
298C23×C139—22no—
299C23×C139—22no—
300C23×C139—21no—
301C23×C139—22no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—22no—
305C23×C139—22no—
306C23×C139—41no—
307C23×C139—44no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139—44no—
316C23×C139—44no—
317C23×C139—44no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—42no—
321C23×C139—42no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139C22×D411yescharacteristic
327C23×C139C22×D411yescharacteristic
328C23×C139C22×D411yescharacteristic
329C23×C139C2×#4111yescharacteristic
330C23×C139C2×#4111yescharacteristic
331C23×C139H(5,𝔽2)11yescharacteristic
332C23×C1392−1+411yescharacteristic
333Q8×C139—42no—
334Q8×C139—81no—
335D4×C139—48no—
336D4×C139—42no—
337D4×C139—42no—
338D4×C139—41no—
339D4×C139—41no—
340D4×C139—41no—
341D4×C139—42no—
342D4×C139—42no—
343D4×C139—41no—
344D4×C139—42no—
345D4×C139—81no—
346D4×C139—82no—
347D4×C139—82no—
348D4×C139—88no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
351C2×C4×C139—22no—
352C2×C4×C139—22no—
353C2×C4×C139—22no—
354C2×C4×C139—22no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—22no—
360C2×C4×C139—22no—
361C2×C4×C139—21no—
362C2×C4×C139—22no—
363C2×C4×C139—21no—
364C2×C4×C139—22no—
365C2×C4×C139—22no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—44no—
370C2×C4×C139—44no—
371C2×C4×C139—44no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—44no—
379C2×C4×C139—42no—
380C2×C4×C139—41no—
381C2×C4×C139—42no—
382C2×C4×C139—41no—
383C2×C4×C139—42no—
384C2×C4×C139—41no—
385C2×C4×C139—42no—
386C2×C4×C139—42no—
387C2×C4×C139—42no—
388C2×C4×C139—41no—
389C2×C4×C139—42no—
390C2×C4×C139—41no—
391C2×C4×C139—42no—
392C2×C4×C139—42no—
393C2×C4×C139—81no—
394C2×C4×C139—82no—
395C2×C4×C139—82no—
396C2×C4×C139#12011yescharacteristic
397C2×C4×C139#12011yescharacteristic
398C2×C4×C139#12011yescharacteristic
399C2×C4×C139#12011yescharacteristic
400C22×C139—21no—
401C22×C139—21no—
402C22×C139—21no—
403C22×C139—21no—
404C22×C139—21no—
405C22×C139—21no—
406C22×C139—24no—
407C22×C139—24no—
408C22×C139—24no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—42no—
414C22×C139—42no—
415C22×C139—42no—
416C22×C139—42no—
417C22×C139—42no—
418C22×C139—42no—
419C22×C139—42no—
420C22×C139—42no—
421C22×C139—42no—
422C22×C139—42no—
423C22×C139—42no—
424C22×C139—42no—
425C22×C139—42no—
426C22×C139—41no—
427C22×C139—42no—
428C22×C139—41no—
429C22×C139—42no—
430C22×C139—42no—
431C22×C139—41no—
432C22×C139—82no—
433C22×C139—81no—
434C22×C139—82no—
435C22×C139C2×#12011yescharacteristic
436C22×C139#52511yescharacteristic
437C22×C139#53711yescharacteristic
438C22×C139#54611yescharacteristic
439C22×C139#54711yescharacteristic
440C22×C139#54811yescharacteristic
441C22×C139#55011yescharacteristic
442C4×C139—21no—
443C4×C139—21no—
444C4×C139—21no—
445C4×C139—42no—
446C4×C139—41no—
447C4×C139—42no—
448C4×C139—42no—
449C4×C139—41no—
450C4×C139—42no—
451C4×C139—41no—
452C4×C139—42no—
453C4×C139—82no—
454C4×C139—81no—
455C4×C139—82no—
456C4×C139B(4,𝔽2)12yes—
457C2×C139—21no—
458C2×C139—21no—
459C2×C139—21no—
460C2×C139—21no—
461C2×C139—21no—
462C2×C139—21no—
463C2×C139—44no—
464C2×C139—81no—
465C2×C139—82no—
466C2×C139#240711yescharacteristic
467C2×C139C2×B(4,𝔽2)11yescharacteristic
468C2×C139#302511yescharacteristic
469#24140C13911yesmaximal, characteristic, direct product factor, Sylow
470C139#2414011yescharacteristic, direct product factor, Sylow
471#3505C2×C13911yescharacteristic, complemented
472#2848C2×C13911yescharacteristic, complemented
473#2847C2×C13911yescharacteristic, complemented
474C4×#120C2×C13911yescharacteristic, complemented
475#2044C2×C13912yescomplemented
476#2021C2×C13912yescomplemented
477#1996C2×C13911yescharacteristic, complemented
478#1964C2×C13911yescharacteristic, complemented
479#1889C2×C13912yescomplemented
480#1867C2×C13912yescomplemented
481#1799C2×C13911yescharacteristic, complemented
482C24×C4C22×C13911yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C13912yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C13911yescharacteristic
496C2×#121—21no—
497C2×#121C22×C13911yescharacteristic
498C2×#120C22×C13911yescharacteristic
499C2×#120C22×C13912yes—
500#518C22×C13912yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C13911yescharacteristic
503C2×#99C22×C13912yes—
504C2×#99C22×C13912yes—
505C2×#99C22×C13912yes—
506#386—22no—
507#386—21no—
508#386C22×C13912yes—
509#386C22×C13911yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C13912yes—
513#385C22×C13911yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C13911yescharacteristic
517#380C22×C13911yescharacteristic
518#379C22×C13912yes—
519#379C22×C13911yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C13911yescharacteristic
522#342C22×C13912yes—
523#342C22×C13912yes—
524#342C22×C13912yes—
525C25C23×C13911yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C13911yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C13911yescharacteristic, complemented
531C22×D4C23×C13911yescharacteristic
532C22×D4C23×C13912yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C13911yescharacteristic, complemented
541C23×C4C23×C13911yescharacteristic
542C23×C4C23×C13911yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C13911yescharacteristic, complemented
597C2×C4⋊C4D4×C13911yescharacteristic, complemented
598C2×C4⋊C4D4×C13911yescharacteristic, complemented
599C2×C4⋊C4D4×C13912yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C13911yescharacteristic, complemented
610C2×C22⋊C4D4×C13912yescomplemented
611C2×C22⋊C4C23×C13912yes—
612C2×C22⋊C4C23×C13911yescharacteristic
613C2×C22⋊C4C23×C13912yes—
614C2×C22⋊C4C23×C13911yescharacteristic
615C2×C22⋊C4C23×C13912yes—
616C2×C22⋊C4C23×C13911yescharacteristic
617C2×C42—21no—
618C2×C42D4×C13911yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C13912yes—
638C24C2×D4×C13911yescharacteristic
639C24#41×C13912yescomplemented
640C24C24×C13911yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C13911yescharacteristic
699C22×C4C2×D4×C13912yes—
700C22×C4C2×D4×C13911yescharacteristic
701C22×C4C2×D4×C13911yescharacteristic
702C22×C4C2×D4×C13911yescharacteristic
703C22×C4C2×D4×C13911yescharacteristic
704C22×C4C2×D4×C13912yes—
705C22×C4C2×D4×C13911yescharacteristic
706C22×C4C2×D4×C13912yes—
707C22×C4C2×D4×C13911yescharacteristic
708C22×C4C2×D4×C13911yescharacteristic
709C22×C4C2×D4×C13911yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C13912yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C13911yescharacteristic
797C23C22×D4×C13911yescharacteristic
798C23C22×D4×C13911yescharacteristic
799C23C2×#41×C13911yescharacteristic
800C23C2×#41×C13911yescharacteristic
801C23H(5,𝔽2)×C13911yescharacteristic
802C232−1+4×C13911yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C13911yescharacteristic
867C2×C4#120×C13911yescharacteristic
868C2×C4#120×C13911yescharacteristic
869C2×C4#120×C13911yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C13911yescharacteristic
906C22#525×C13911yescharacteristic
907C22#537×C13911yescharacteristic
908C22#546×C13911yescharacteristic
909C22#547×C13911yescharacteristic
910C22#548×C13911yescharacteristic
911C22#550×C13911yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C13912yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2#2407×C13911yescharacteristic
937C2C2×B(4,𝔽2)×C13911yescharacteristic
938C2#3025×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC24C24×C139
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C139C2semidirect
2. #2848×C139C2semidirect
3. #2847×C139C2semidirect
4. C4×#120×C139C2semidirect
5. #2044×C139C2semidirect
6. #2021×C139C2semidirect
7. #1996×C139C2semidirect
8. #1964×C139C2semidirect
9. #1889×C139C2semidirect
10. #1867×C139C2semidirect
11. #1799×C139C2semidirect
57. C22×Q8×C139D4semidirect
60. C22×D4×C139D4semidirect
70. C23×C4×C139D4semidirect
126. C2×C4⋊C4×C139D4semidirect
127. C2×C4⋊C4×C139D4semidirect
128. C2×C4⋊C4×C139D4semidirect
129. C2×C4⋊C4×C139D4semidirect
139. C2×C22⋊C4×C139D4semidirect
140. C2×C22⋊C4×C139D4semidirect
148. C2×C42×C139D4semidirect
169. C24×C139#41semidirect
285. C22⋊C4×C139#41semidirect
469. #24140C139direct (N × H)
470. C139#24140direct (N × H)
471. #3505C2×C139semidirect
472. #2848C2×C139semidirect
473. #2847C2×C139semidirect
474. C4×#120C2×C139semidirect
475. #2044C2×C139semidirect
476. #2021C2×C139semidirect
477. #1996C2×C139semidirect
478. #1964C2×C139semidirect
479. #1889C2×C139semidirect
480. #1867C2×C139semidirect
481. #1799C2×C139semidirect
527. C22×Q8D4×C139semidirect
530. C22×D4D4×C139semidirect
540. C23×C4D4×C139semidirect
596. C2×C4⋊C4D4×C139semidirect
597. C2×C4⋊C4D4×C139semidirect
598. C2×C4⋊C4D4×C139semidirect
599. C2×C4⋊C4D4×C139semidirect
609. C2×C22⋊C4D4×C139semidirect
610. C2×C22⋊C4D4×C139semidirect
618. C2×C42D4×C139semidirect
639. C24#41×C139semidirect
755. C22⋊C4#41×C139semidirect

Maximal subgroups

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

subgroupindex
#3505×C1392
#2848×C1392
#2847×C1392
C4×#120×C1392
#2044×C1392
#2021×C1392
#1996×C1392
#1964×C1392
#1889×C1392
#1867×C1392
#1799×C1392
#24140139