Finite Group Databasebeta

← C139×#25587 #48020183

Subgroups — C139×#25587 #48020183

Order 35584.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C139C211yesmaximal, characteristic, complemented
2#2561×C139C211yesmaximal, characteristic, complemented
3#2539×C139C211yesmaximal, characteristic, complemented
4#2534×C139C211yesmaximal, characteristic, complemented
5#2022×C139C212yesmaximal, complemented
6#2021×C139C212yesmaximal, complemented
7#1996×C139C211yesmaximal, characteristic, complemented
8#1964×C139C211yesmaximal, characteristic, complemented
9#1890×C139C212yesmaximal, complemented
10#1889×C139C212yesmaximal, complemented
11C4×#99×C139C211yesmaximal, characteristic, complemented
12#553×C139—21no—
13#553×C139—22no—
14#552×C139—21no—
15#551×C139—22no—
16#548×C139—21no—
17#546×C139—21no—
18#539×C139—21no—
19#538×C139—21no—
20#534×C139C2212yes—
21#529×C139—21no—
22#525×C139—21no—
23C2×#123×C139C2212yes—
24C2×#123×C139C2211yescharacteristic
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#120×C139C2212yes—
28C2×#120×C139C2211yescharacteristic
29#518×C139C2212yes—
30C2×C4×D4×C139C2211yescharacteristic
31C22×C22⋊C4×C139C2211yescharacteristic
32C2×#99×C139C2212yes—
33C2×#99×C139C2212yes—
34C2×#99×C139C2212yes—
35#399×C139—21no—
36#397×C139—21no—
37#396×C139—21no—
38#394×C139—21no—
39#393×C139—21no—
40#392×C139—21no—
41#390×C139—22no—
42#388×C139—22no—
43#388×C139—21no—
44#386×C139—21no—
45#381×C139C2212yes—
46#381×C139C2211yescharacteristic
47#380×C139C2211yescharacteristic
48#379×C139C2212yes—
49#379×C139C2211yescharacteristic
50C4×C22⋊C4×C139C2211yescharacteristic
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×C139D411yescharacteristic, complemented
64C23×C4×C139C2311yescharacteristic
65C23×C4×C139C2311yescharacteristic
66#126×C139—22no—
67#126×C139—22no—
68#126×C139—22no—
69#125×C139—21no—
70#125×C139—22no—
71#124×C139—21no—
72#124×C139—22no—
73#123×C139—22no—
74#123×C139—22no—
75#123×C139—22no—
76#123×C139—22no—
77#123×C139—22no—
78#123×C139—24no—
79#123×C139—42no—
80#123×C139—42no—
81C22⋊Q8×C139—21no—
82C22⋊Q8×C139—22no—
83C22⋊Q8×C139—21no—
84C22⋊Q8×C139—21no—
85C22⋊Q8×C139—21no—
86C22⋊Q8×C139—21no—
87#121×C139—21no—
88#121×C139—22no—
89#121×C139—21no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—22no—
94#121×C139—22no—
95#120×C139—22no—
96#120×C139—22no—
97#120×C139—24no—
98#120×C139—42no—
99#120×C139—42no—
100C4×Q8×C139—21no—
101C4×D4×C139—22no—
102C4×D4×C139—21no—
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139—21no—
106C4×D4×C139—21no—
107C4×D4×C139—22no—
108C4×D4×C139—22no—
109C4×D4×C139—22no—
110C4×D4×C139—22no—
111#117×C139—21no—
112#117×C139—22no—
113#117×C139—22no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—22no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139D411yescharacteristic, complemented
118C2×C4⋊C4×C139D411yescharacteristic, complemented
119C2×C4⋊C4×C139D411yescharacteristic, complemented
120C2×C4⋊C4×C139D412yescomplemented
121C2×C22⋊C4×C139—22no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—22no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—22no—
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—21no—
135C2×C22⋊C4×C139—22no—
136C2×C22⋊C4×C139D411yescharacteristic, complemented
137C2×C22⋊C4×C139D412yescomplemented
138C2×C22⋊C4×C139C2312yes—
139C2×C22⋊C4×C139C2311yescharacteristic
140C2×C22⋊C4×C139C2311yescharacteristic
141C2×C22⋊C4×C139C2311yescharacteristic
142C2×C22⋊C4×C139C2312yes—
143C2×C22⋊C4×C139C2312yes—
144C2×C42×C139—21no—
145C2×C42×C139—21no—
146C2×C42×C139D411yescharacteristic, complemented
147#99×C139—24no—
148#99×C139—42no—
149#99×C139—42no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—22no—
153#95×C139—21no—
154#95×C139—21no—
155#95×C139—22no—
156#95×C139—21no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—22no—
161C24×C139—22no—
162C24×C139—42no—
163C24×C139—81no—
164C24×C139C2×D412yes—
165C24×C139C2×D411yescharacteristic
166C24×C139C2411yescharacteristic
167#41×C139—82no—
168C2×Q8×C139—21no—
169C2×Q8×C139—21no—
170C2×Q8×C139—81no—
171C2×D4×C139—21no—
172C2×D4×C139—22no—
173C2×D4×C139—21no—
174C2×D4×C139—22no—
175C2×D4×C139—22no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—22no—
179C2×D4×C139—22no—
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—22no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—44no—
186C2×D4×C139—42no—
187C2×D4×C139—44no—
188C2×D4×C139—42no—
189C2×D4×C139—81no—
190C2×D4×C139—82no—
191C2×D4×C139—81no—
192C22×C4×C139—22no—
193C22×C4×C139—22no—
194C22×C4×C139—22no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—22no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—22no—
204C22×C4×C139—22no—
205C22×C4×C139—81no—
206C22×C4×C139—81no—
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D412yes—
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D412yes—
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D412yes—
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C4⋊C4×C139—22no—
220C4⋊C4×C139—22no—
221C4⋊C4×C139—22no—
222C4⋊C4×C139—22no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—22no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—22no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—44no—
232C4⋊C4×C139—42no—
233C4⋊C4×C139—81no—
234C22⋊C4×C139—22no—
235C22⋊C4×C139—22no—
236C22⋊C4×C139—22no—
237C22⋊C4×C139—22no—
238C22⋊C4×C139—22no—
239C22⋊C4×C139—22no—
240C22⋊C4×C139—21no—
241C22⋊C4×C139—22no—
242C22⋊C4×C139—21no—
243C22⋊C4×C139—22no—
244C22⋊C4×C139—22no—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—21no—
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—44no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—44no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—41no—
260C22⋊C4×C139—41no—
261C22⋊C4×C139—41no—
262C22⋊C4×C139—41no—
263C22⋊C4×C139—81no—
264C22⋊C4×C139—82no—
265C22⋊C4×C139#4114yescomplemented
266C42×C139—22no—
267C42×C139—22no—
268C42×C139—21no—
269C42×C139—21no—
270C42×C139—81no—
271C42×C139—81no—
272C23×C139—22no—
273C23×C139—22no—
274C23×C139—22no—
275C23×C139—22no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—22no—
280C23×C139—22no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—42no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—42no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—42no—
293C23×C139—42no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—42no—
298C23×C139—42no—
299C23×C139—84no—
300C23×C139—84no—
301C23×C139C22×D411yescharacteristic
302C23×C139C22×D411yescharacteristic
303C23×C139C22×D411yescharacteristic
304C23×C139C2×#4112yes—
305C23×C139H(5,𝔽2)12yes—
306Q8×C139—42no—
307Q8×C139—81no—
308D4×C139—42no—
309D4×C139—42no—
310D4×C139—42no—
311D4×C139—42no—
312D4×C139—42no—
313D4×C139—42no—
314D4×C139—42no—
315D4×C139—81no—
316D4×C139—82no—
317D4×C139—82no—
318D4×C139—88no—
319D4×C139—84no—
320C2×C4×C139—21no—
321C2×C4×C139—22no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—24no—
329C2×C4×C139—22no—
330C2×C4×C139—22no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—42no—
338C2×C4×C139—42no—
339C2×C4×C139—42no—
340C2×C4×C139—41no—
341C2×C4×C139—42no—
342C2×C4×C139—41no—
343C2×C4×C139—42no—
344C2×C4×C139—42no—
345C2×C4×C139—42no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—42no—
356C2×C4×C139—42no—
357C2×C4×C139—42no—
358C2×C4×C139—81no—
359C2×C4×C139—82no—
360C2×C4×C139—82no—
361C2×C4×C139#12011yescharacteristic
362C2×C4×C139#12011yescharacteristic
363C2×C4×C139#12011yescharacteristic
364C2×C4×C139#12011yescharacteristic
365C22×C139—21no—
366C22×C139—21no—
367C22×C139—21no—
368C22×C139—21no—
369C22×C139—21no—
370C22×C139—21no—
371C22×C139—42no—
372C22×C139—42no—
373C22×C139—42no—
374C22×C139—44no—
375C22×C139—42no—
376C22×C139—44no—
377C22×C139—42no—
378C22×C139—41no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—42no—
383C22×C139—41no—
384C22×C139—42no—
385C22×C139—82no—
386C22×C139—82no—
387C22×C139—81no—
388C22×C139—82no—
389C22×C139—81no—
390C22×C139—82no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139C2×#12011yescharacteristic
395C22×C139#53211yescharacteristic
396C22×C139#53511yescharacteristic
397C22×C139#54612yes—
398C22×C139#55012yes—
399C4×C139—21no—
400C4×C139—21no—
401C4×C139—21no—
402C4×C139—21no—
403C4×C139—44no—
404C4×C139—41no—
405C4×C139—42no—
406C4×C139—41no—
407C4×C139—42no—
408C4×C139—41no—
409C4×C139—42no—
410C4×C139—81no—
411C4×C139—82no—
412C4×C139—81no—
413C4×C139—81no—
414C2×C139—22no—
415C2×C139—21no—
416C2×C139—22no—
417C2×C139—21no—
418C2×C139—82no—
419C2×C139—81no—
420C2×C139—82no—
421C2×C139#243111yescharacteristic
422C2×C139#302511yescharacteristic
423C2×C139#302611yescharacteristic
424#25587C13911yesmaximal, characteristic, direct product factor, Sylow
425C139#2558711yescharacteristic, direct product factor, Sylow
426#3505C2×C13911yescharacteristic, complemented
427#2561C2×C13911yescharacteristic, complemented
428#2539C2×C13911yescharacteristic, complemented
429#2534C2×C13911yescharacteristic, complemented
430#2022C2×C13912yescomplemented
431#2021C2×C13912yescomplemented
432#1996C2×C13911yescharacteristic, complemented
433#1964C2×C13911yescharacteristic, complemented
434#1890C2×C13912yescomplemented
435#1889C2×C13912yescomplemented
436C4×#99C2×C13911yescharacteristic, complemented
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C13912yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C13912yes—
449C2×#123C22×C13911yescharacteristic
450C2×C22⋊Q8C22×C13911yescharacteristic
451C2×#121C22×C13911yescharacteristic
452C2×#120C22×C13912yes—
453C2×#120C22×C13911yescharacteristic
454#518C22×C13912yes—
455C2×C4×D4C22×C13911yescharacteristic
456C22×C22⋊C4C22×C13911yescharacteristic
457C2×#99C22×C13912yes—
458C2×#99C22×C13912yes—
459C2×#99C22×C13912yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C13912yes—
471#381C22×C13911yescharacteristic
472#380C22×C13911yescharacteristic
473#379C22×C13912yes—
474#379C22×C13911yescharacteristic
475C4×C22⋊C4C22×C13911yescharacteristic
476C4×C22⋊C4C22×C13911yescharacteristic
477#342C22×C13912yes—
478#342C22×C13912yes—
479#342C22×C13912yes—
480C25C23×C13911yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C13911yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C13911yescharacteristic, complemented
486C22×D4C23×C13911yescharacteristic
487C22×D4C23×C13912yes—
488C23×C4D4×C13911yescharacteristic, complemented
489C23×C4C23×C13911yescharacteristic
490C23×C4C23×C13911yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C13911yescharacteristic, complemented
543C2×C4⋊C4D4×C13911yescharacteristic, complemented
544C2×C4⋊C4D4×C13912yescomplemented
545C2×C4⋊C4D4×C13911yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C13911yescharacteristic, complemented
562C2×C22⋊C4D4×C13912yescomplemented
563C2×C22⋊C4C23×C13911yescharacteristic
564C2×C22⋊C4C23×C13911yescharacteristic
565C2×C22⋊C4C23×C13912yes—
566C2×C22⋊C4C23×C13911yescharacteristic
567C2×C22⋊C4C23×C13912yes—
568C2×C22⋊C4C23×C13912yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C13911yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C13912yes—
590C24C2×D4×C13911yescharacteristic
591C24C24×C13911yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13912yes—
634C22×C4C2×D4×C13911yescharacteristic
635C22×C4C2×D4×C13912yes—
636C22×C4C2×D4×C13911yescharacteristic
637C22×C4C2×D4×C13912yes—
638C22×C4C2×D4×C13911yescharacteristic
639C22×C4C2×D4×C13911yescharacteristic
640C22×C4C2×D4×C13911yescharacteristic
641C22×C4C2×D4×C13911yescharacteristic
642C22×C4C2×D4×C13911yescharacteristic
643C22×C4C2×D4×C13911yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C13914yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C13911yescharacteristic
727C23C22×D4×C13911yescharacteristic
728C23C22×D4×C13911yescharacteristic
729C23C2×#41×C13912yes—
730C23H(5,𝔽2)×C13912yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C13911yescharacteristic
787C2×C4#120×C13911yescharacteristic
788C2×C4#120×C13911yescharacteristic
789C2×C4#120×C13911yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C13911yescharacteristic
820C22#532×C13911yescharacteristic
821C22#535×C13911yescharacteristic
822C22#546×C13912yes—
823C22#550×C13912yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2#2431×C13911yescharacteristic
847C2#3025×C13911yescharacteristic
848C2#3026×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. #2561×C139C2semidirect
3. #2539×C139C2semidirect
4. #2534×C139C2semidirect
5. #2022×C139C2semidirect
6. #2021×C139C2semidirect
7. #1996×C139C2semidirect
8. #1964×C139C2semidirect
9. #1890×C139C2semidirect
10. #1889×C139C2semidirect
11. C4×#99×C139C2semidirect
57. C22×Q8×C139D4semidirect
60. C22×D4×C139D4semidirect
63. C23×C4×C139D4semidirect
117. C2×C4⋊C4×C139D4semidirect
118. C2×C4⋊C4×C139D4semidirect
119. C2×C4⋊C4×C139D4semidirect
120. C2×C4⋊C4×C139D4semidirect
136. C2×C22⋊C4×C139D4semidirect
137. C2×C22⋊C4×C139D4semidirect
146. C2×C42×C139D4semidirect
265. C22⋊C4×C139#41semidirect
424. #25587C139direct (N × H)
425. C139#25587direct (N × H)
426. #3505C2×C139semidirect
427. #2561C2×C139semidirect
428. #2539C2×C139semidirect
429. #2534C2×C139semidirect
430. #2022C2×C139semidirect
431. #2021C2×C139semidirect
432. #1996C2×C139semidirect
433. #1964C2×C139semidirect
434. #1890C2×C139semidirect
435. #1889C2×C139semidirect
436. C4×#99C2×C139semidirect
482. C22×Q8D4×C139semidirect
485. C22×D4D4×C139semidirect
488. C23×C4D4×C139semidirect
542. C2×C4⋊C4D4×C139semidirect
543. C2×C4⋊C4D4×C139semidirect
544. C2×C4⋊C4D4×C139semidirect
545. C2×C4⋊C4D4×C139semidirect
561. C2×C22⋊C4D4×C139semidirect
562. C2×C22⋊C4D4×C139semidirect
571. C2×C42D4×C139semidirect
690. 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
#2561×C1392
#2539×C1392
#2534×C1392
#2022×C1392
#2021×C1392
#1996×C1392
#1964×C1392
#1890×C1392
#1889×C1392
C4×#99×C1392
#25587139