Finite Group Databasebeta

← C2×#2009×C139 #48018007

Subgroups — C2×#2009×C139 #48018007

Order 35584.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic
2C22×#137×C139C211yesmaximal, characteristic, complemented
3C2×#536×C139C211yesmaximal, characteristic, complemented
4C2×#421×C139C211yesmaximal, characteristic, complemented
5C2×#419×C139C211yesmaximal, characteristic, complemented
6C2×#410×C139C211yesmaximal, characteristic, complemented
7#2009×C139C218yesmaximal, direct product factor
8C2×#344×C139C211yesmaximal, characteristic, complemented
9C22×#41×C139C2211yescharacteristic
10C22×#41×C139C2211yescharacteristic
11C23×Q8×C139C2211yescharacteristic
12#575×C139—22no—
13#575×C139—22no—
14#575×C139—22no—
15#575×C139C2214yes—
16C2×#137×C139—22no—
17C2×#137×C139—22no—
18C2×#137×C139—22no—
19C2×#137×C139—21no—
20C2×#137×C139—21no—
21C2×#137×C139—22no—
22C2×#137×C139—22no—
23C2×#137×C139C2214yescomplemented
24C2×AGL(1,ℤ/8)×C139—21no—
25C2×AGL(1,ℤ/8)×C139—21no—
26C2×#135×C139—22no—
27C22×Q16×C139—21no—
28C22×SD16×C139—21no—
29C22×M16×C139C2211yescharacteristic
30C22×M16×C139C2211yescharacteristic
31#536×C139—22no—
32#536×C139—22no—
33#536×C139—22no—
34#536×C139C2214yescomplemented
35C2×C4⋊Q8×C139—21no—
36C2×#124×C139—21no—
37C2×#123×C139—22no—
38C2×C22⋊Q8×C139—22no—
39C2×#117×C139C2211yescharacteristic
40C2×#117×C139C2211yescharacteristic
41#421×C139—22no—
42#421×C139C2214yescomplemented
43C2×#104×C139—22no—
44#419×C139—22no—
45#419×C139C2214yescomplemented
46C2×#103×C139—22no—
47#410×C139—22no—
48#410×C139C2214yescomplemented
49C2×#99×C139—22no—
50#344×C139C2214yescomplemented
51C2×#41×C139—21no—
52C2×#41×C139—21no—
53C2×#41×C139—21no—
54C2×#41×C139—21no—
55C2×#41×C139—21no—
56C2×#41×C139—21no—
57C2×#41×C139—21no—
58C2×#41×C139—21no—
59C2×#41×C139—21no—
60C2×#41×C139—21no—
61C2×#41×C139—21no—
62C2×#41×C139—21no—
63C2×#41×C139—21no—
64C2×#41×C139—21no—
65C2×#41×C139—21no—
66C2×#41×C139—21no—
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71C2×#41×C139D412yes—
72C2×#41×C139D412yes—
73C2×#41×C139C2312yes—
74C2×#41×C139C2312yes—
75C22×Q8×C139—21no—
76C22×Q8×C139—21no—
77C22×Q8×C139—21no—
78C22×Q8×C139—21no—
79C22×Q8×C139—21no—
80C22×Q8×C139—21no—
81C22×Q8×C139—21no—
82C22×Q8×C139—21no—
83C22×Q8×C139—21no—
84C22×Q8×C139—21no—
85C22×Q8×C139—21no—
86C22×Q8×C139D412yes—
87C22×Q8×C139D411yescharacteristic
88C22×Q8×C139D412yes—
89C22×Q8×C139D411yescharacteristic
90C22×Q8×C139C2312yes—
91C22×D4×C139—21no—
92C22×D4×C139—21no—
93C22×D4×C139D411yescharacteristic
94C22×D4×C139D411yescharacteristic
95C23×C4×C139—21no—
96C23×C4×C139—21no—
97C23×C4×C139—21no—
98C23×C4×C139C2311yescharacteristic
99#137×C139—28no—
100#137×C139—28no—
101#137×C139—24no—
102#137×C139—24no—
103#137×C139—28no—
104#137×C139—24no—
105#137×C139—24no—
106#137×C139—28no—
107AGL(1,ℤ/8)×C139—24no—
108AGL(1,ℤ/8)×C139—24no—
109AGL(1,ℤ/8)×C139—24no—
110AGL(1,ℤ/8)×C139—24no—
111#135×C139—28no—
112#135×C139—28no—
113C2×Q16×C139—24no—
114C2×Q16×C139—24no—
115C2×Q16×C139—22no—
116C2×Q16×C139—24no—
117C2×SD16×C139—24no—
118C2×SD16×C139—24no—
119C2×SD16×C139—22no—
120C2×SD16×C139—22no—
121C2×SD16×C139—24no—
122C2×D8×C139—22no—
123C2×M16×C139—21no—
124C2×M16×C139—21no—
125C2×M16×C139—21no—
126C2×M16×C139—21no—
127C2×M16×C139—21no—
128C2×M16×C139—21no—
129C2×M16×C139—21no—
130C2×M16×C139D412yes—
131C2×M16×C139D412yes—
132C2×M16×C139D412yes—
133C2×M16×C139C2312yes—
134C2×M16×C139C2312yes—
135C22×C8×C139—21no—
136C22×C8×C139D412yes—
137C4⋊Q8×C139—24no—
138C4⋊Q8×C139—24no—
139#124×C139—24no—
140#124×C139—24no—
141#123×C139—28no—
142#123×C139—28no—
143C22⋊Q8×C139—28no—
144C22⋊Q8×C139—28no—
145#117×C139—21no—
146#117×C139—21no—
147#117×C139—21no—
148#117×C139—21no—
149#117×C139—21no—
150#117×C139D412yes—
151#117×C139C2312yes—
152#117×C139C2312yes—
153C2×C4⋊C4×C139—24no—
154C2×C4⋊C4×C139—21no—
155C2×C4⋊C4×C139—21no—
156C2×C22⋊C4×C139—24no—
157C2×C22⋊C4×C139—21no—
158C2×C22⋊C4×C139D412yes—
159C2×C42×C139—21no—
160C2×C42×C139—21no—
161#104×C139—28no—
162#103×C139—28no—
163#99×C139—28no—
164C24×C139—21no—
165C24×C139—21no—
166C24×C139C2×D411yescharacteristic
167#41×C139—22no—
168#41×C139—22no—
169#41×C139—22no—
170#41×C139—22no—
171#41×C139—22no—
172#41×C139—22no—
173#41×C139—22no—
174#41×C139—22no—
175#41×C139—22no—
176#41×C139—22no—
177#41×C139—22no—
178#41×C139—22no—
179#41×C139—22no—
180#41×C139—22no—
181#41×C139—22no—
182#41×C139—22no—
183#41×C139—41no—
184#41×C139—41no—
185#41×C139—41no—
186#41×C139—41no—
187#41×C139—41no—
188#41×C139—41no—
189#41×C139—41no—
190#41×C139—41no—
191#41×C139—41no—
192#41×C139—41no—
193#41×C139—41no—
194#41×C139—41no—
195#41×C139—41no—
196#41×C139—41no—
197#41×C139—41no—
198#41×C139—41no—
199C2×Q8×C139—22no—
200C2×Q8×C139—22no—
201C2×Q8×C139—21no—
202C2×Q8×C139—21no—
203C2×Q8×C139—22no—
204C2×Q8×C139—22no—
205C2×Q8×C139—22no—
206C2×Q8×C139—21no—
207C2×Q8×C139—21no—
208C2×Q8×C139—21no—
209C2×Q8×C139—21no—
210C2×Q8×C139—22no—
211C2×Q8×C139—22no—
212C2×Q8×C139—21no—
213C2×Q8×C139—21no—
214C2×Q8×C139—22no—
215C2×Q8×C139—22no—
216C2×Q8×C139—22no—
217C2×Q8×C139—22no—
218C2×Q8×C139—21no—
219C2×Q8×C139—21no—
220C2×Q8×C139—22no—
221C2×Q8×C139—22no—
222C2×Q8×C139—22no—
223C2×Q8×C139—22no—
224C2×Q8×C139—41no—
225C2×Q8×C139—41no—
226C2×Q8×C139—41no—
227C2×Q8×C139—41no—
228C2×Q8×C139—41no—
229C2×Q8×C139—41no—
230C2×Q8×C139—41no—
231C2×Q8×C139—41no—
232C2×Q8×C139—41no—
233C2×Q8×C139—41no—
234C2×Q8×C139—41no—
235C2×Q8×C139—41no—
236C2×Q8×C139C2×D414yes—
237C2×Q8×C139C2×D412yes—
238C2×Q8×C139C2×D412yes—
239C2×D4×C139—22no—
240C2×D4×C139—22no—
241C2×D4×C139—22no—
242C2×D4×C139—22no—
243C2×D4×C139—21no—
244C2×D4×C139—21no—
245C2×D4×C139—21no—
246C2×D4×C139—21no—
247C2×D4×C139—21no—
248C2×D4×C139—21no—
249C2×D4×C139—21no—
250C2×D4×C139—21no—
251C2×D4×C139—21no—
252C2×D4×C139—21no—
253C2×D4×C139—41no—
254C2×D4×C139—41no—
255C2×D4×C139—41no—
256C2×D4×C139—41no—
257C2×D4×C139—41no—
258C2×D4×C139—41no—
259C2×D4×C139—41no—
260C2×D4×C139—41no—
261C2×D4×C139C2×D412yes—
262C2×D4×C139C2×D412yes—
263C22×C4×C139—22no—
264C22×C4×C139—22no—
265C22×C4×C139—21no—
266C22×C4×C139—22no—
267C22×C4×C139—21no—
268C22×C4×C139—22no—
269C22×C4×C139—22no—
270C22×C4×C139—22no—
271C22×C4×C139—22no—
272C22×C4×C139—22no—
273C22×C4×C139—41no—
274C22×C4×C139—41no—
275C22×C4×C139—41no—
276C22×C4×C139—41no—
277C22×C4×C139—41no—
278C22×C4×C139—41no—
279C22×C4×C139—41no—
280C22×C4×C139—41no—
281C22×C4×C139—41no—
282C22×C4×C139—41no—
283C22×C4×C139—41no—
284C22×C4×C139—41no—
285C22×C4×C139—41no—
286C22×C4×C139C2×D411yescharacteristic
287C22×C4×C139C2×D411yescharacteristic
288C22×C4×C139C2×D411yescharacteristic
289C22×C4×C139C2×D411yescharacteristic
290C22×C4×C139C2×D411yescharacteristic
291C22×C4×C139C2×D411yescharacteristic
292C22×C4×C139C2×D411yescharacteristic
293C22×C4×C139C2×D411yescharacteristic
294C22×C4×C139C2×D411yescharacteristic
295C22×C4×C139C2×D411yescharacteristic
296C22×C4×C139C2×D411yescharacteristic
297C22×C4×C139#4111yescharacteristic
298C22×C4×C139#4111yescharacteristic
299C22×C4×C139C2411yescharacteristic
300Q16×C139—216no—
301Q16×C139—28no—
302SD16×C139—216no—
303SD16×C139—28no—
304SD16×C139—28no—
305D8×C139—28no—
306M16×C139—22no—
307M16×C139—22no—
308M16×C139—22no—
309M16×C139—22no—
310M16×C139—22no—
311M16×C139—22no—
312M16×C139—22no—
313M16×C139C2×D414yes—
314C2×C8×C139—22no—
315C2×C8×C139—22no—
316C2×C8×C139—22no—
317C2×C8×C139—22no—
318C2×C8×C139—22no—
319C2×C8×C139C2×D414yes—
320C4⋊C4×C139—216no—
321C4⋊C4×C139—22no—
322C4⋊C4×C139—22no—
323C4⋊C4×C139—22no—
324C4⋊C4×C139—41no—
325C22⋊C4×C139—216no—
326C22⋊C4×C139—22no—
327C22⋊C4×C139—22no—
328C22⋊C4×C139—41no—
329C22⋊C4×C139C2×D414yes—
330C42×C139—22no—
331C42×C139—22no—
332C42×C139—22no—
333C42×C139—41no—
334C23×C139—22no—
335C23×C139—22no—
336C23×C139—42no—
337C23×C139—44no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—82no—
343C23×C139#12011yescharacteristic
344C23×C139#12011yescharacteristic
345C23×C139#12111yescharacteristic
346C23×C139#12111yescharacteristic
347C23×C139#12711yescharacteristic
348C23×C139#12711yescharacteristic
349C23×C139C22×D411yescharacteristic
350Q8×C139—24no—
351Q8×C139—22no—
352Q8×C139—22no—
353Q8×C139—22no—
354Q8×C139—24no—
355Q8×C139—22no—
356Q8×C139—42no—
357Q8×C139—42no—
358Q8×C139—42no—
359Q8×C139—42no—
360Q8×C139—42no—
361Q8×C139—42no—
362Q8×C139—41no—
363Q8×C139—41no—
364Q8×C139—41no—
365Q8×C139—41no—
366D4×C139—22no—
367D4×C139—22no—
368D4×C139—22no—
369D4×C139—22no—
370D4×C139—42no—
371D4×C139—42no—
372D4×C139—42no—
373D4×C139—42no—
374D4×C139—42no—
375D4×C139—42no—
376D4×C139—42no—
377D4×C139—42no—
378D4×C139—41no—
379D4×C139—41no—
380D4×C139—41no—
381D4×C139—41no—
382C2×C4×C139—24no—
383C2×C4×C139—24no—
384C2×C4×C139—22no—
385C2×C4×C139—22no—
386C2×C4×C139—44no—
387C2×C4×C139—42no—
388C2×C4×C139—42no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—42no—
392C2×C4×C139—42no—
393C2×C4×C139—42no—
394C2×C4×C139—41no—
395C2×C4×C139—41no—
396C2×C4×C139—42no—
397C2×C4×C139—42no—
398C2×C4×C139—42no—
399C2×C4×C139—42no—
400C2×C4×C139—42no—
401C2×C4×C139—42no—
402C2×C4×C139—42no—
403C2×C4×C139—42no—
404C2×C4×C139—42no—
405C2×C4×C139—42no—
406C2×C4×C139—82no—
407C2×C4×C139#12011yescharacteristic
408C2×C4×C139#12011yescharacteristic
409C2×C4×C139#12011yescharacteristic
410C2×C4×C139#12011yescharacteristic
411C2×C4×C139#12011yescharacteristic
412C2×C4×C139#12011yescharacteristic
413C2×C4×C139#12011yescharacteristic
414C2×C4×C139#12011yescharacteristic
415C2×C4×C139#12011yescharacteristic
416C2×C4×C139#12011yescharacteristic
417C2×C4×C139#12111yescharacteristic
418C2×C4×C139#12111yescharacteristic
419C2×C4×C139#12111yescharacteristic
420C2×C4×C139#12111yescharacteristic
421C2×C4×C139#12111yescharacteristic
422C2×C4×C139#12111yescharacteristic
423C2×C4×C139#12111yescharacteristic
424C2×C4×C139#12111yescharacteristic
425C2×C4×C139#12111yescharacteristic
426C2×C4×C139#12111yescharacteristic
427C2×C4×C139#12711yescharacteristic
428C2×C4×C139#12711yescharacteristic
429C2×C4×C139C22×D411yescharacteristic
430C2×C4×C139C22×D411yescharacteristic
431C2×C4×C139C22×D411yescharacteristic
432C2×C4×C139C22×D411yescharacteristic
433C2×C4×C139C22×D411yescharacteristic
434C2×C4×C139C2×#4111yescharacteristic
435C8×C139—24no—
436C8×C139—24no—
437C22×C139—22no—
438C22×C139—22no—
439C22×C139—22no—
440C22×C139—41no—
441C22×C139—41no—
442C22×C139—41no—
443C22×C139—41no—
444C22×C139—44no—
445C22×C139—42no—
446C22×C139—42no—
447C22×C139—82no—
448C22×C139—82no—
449C22×C139—82no—
450C22×C139—82no—
451C22×C139—82no—
452C22×C139#39211yescharacteristic
453C22×C139#39211yescharacteristic
454C22×C139#39211yescharacteristic
455C22×C139#39211yescharacteristic
456C22×C139C2×#12011yescharacteristic
457C22×C139C2×#12111yescharacteristic
458C22×C139C2×#12711yescharacteristic
459C4×C139—44no—
460C4×C139—42no—
461C4×C139—42no—
462C4×C139—44no—
463C4×C139—82no—
464C4×C139#39211yescharacteristic
465C4×C139#39211yescharacteristic
466C4×C139#39211yescharacteristic
467C4×C139#39211yescharacteristic
468C4×C139C2×#12011yescharacteristic
469C4×C139C2×#12011yescharacteristic
470C4×C139C2×#12111yescharacteristic
471C4×C139C2×#12111yescharacteristic
472C2×C139—21no—
473C2×C139—21no—
474C2×C139—21no—
475C2×C139—21no—
476C2×C139—21no—
477C2×C139—21no—
478C2×C139—82no—
479C2×C139—82no—
480C2×C139#200912yesdirect product factor
481C2×C139C2×#39211yescharacteristic
482C2×#2009C13911yesmaximal, characteristic, direct product factor, Sylow
483C139C2×#200911yescharacteristic, direct product factor, Sylow
484C2×#575C2×C13911yescharacteristic
485C22×#137C2×C13911yescharacteristic, complemented
486C2×#536C2×C13911yescharacteristic, complemented
487C2×#421C2×C13911yescharacteristic, complemented
488C2×#419C2×C13911yescharacteristic, complemented
489C2×#410C2×C13911yescharacteristic, complemented
490#2009C2×C13918yesdirect product factor
491C2×#344C2×C13911yescharacteristic, complemented
492C22×#41C22×C13911yescharacteristic
493C22×#41C22×C13911yescharacteristic
494C23×Q8C22×C13911yescharacteristic
495#575—22no—
496#575—22no—
497#575—22no—
498#575C22×C13914yes—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—22no—
502C2×#137—21no—
503C2×#137—21no—
504C2×#137—22no—
505C2×#137—22no—
506C2×#137C22×C13914yescomplemented
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)—21no—
509C2×#135—22no—
510C22×Q16—21no—
511C22×SD16—21no—
512C22×M16C22×C13911yescharacteristic
513C22×M16C22×C13911yescharacteristic
514#536—22no—
515#536—22no—
516#536—22no—
517#536C22×C13914yescomplemented
518C2×C4⋊Q8—21no—
519C2×#124—21no—
520C2×#123—22no—
521C2×C22⋊Q8—22no—
522C2×#117C22×C13911yescharacteristic
523C2×#117C22×C13911yescharacteristic
524#421—22no—
525#421C22×C13914yescomplemented
526C2×#104—22no—
527#419—22no—
528#419C22×C13914yescomplemented
529C2×#103—22no—
530#410—22no—
531#410C22×C13914yescomplemented
532C2×#99—22no—
533#344C22×C13914yescomplemented
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41D4×C13912yes—
555C2×#41D4×C13912yes—
556C2×#41C23×C13912yes—
557C2×#41C23×C13912yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8D4×C13912yes—
570C22×Q8D4×C13911yescharacteristic
571C22×Q8D4×C13912yes—
572C22×Q8D4×C13911yescharacteristic
573C22×Q8C23×C13912yes—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4D4×C13911yescharacteristic
577C22×D4D4×C13911yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C13911yescharacteristic
582#137—28no—
583#137—28no—
584#137—24no—
585#137—24no—
586#137—28no—
587#137—24no—
588#137—24no—
589#137—28no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—22no—
599C2×Q16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—24no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—21no—
613C2×M16D4×C13912yes—
614C2×M16D4×C13912yes—
615C2×M16D4×C13912yes—
616C2×M16C23×C13912yes—
617C2×M16C23×C13912yes—
618C22×C8—21no—
619C22×C8D4×C13912yes—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622#124—24no—
623#124—24no—
624#123—28no—
625#123—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117D4×C13912yes—
634#117C23×C13912yes—
635#117C23×C13912yes—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C13912yes—
642C2×C42—21no—
643C2×C42—21no—
644#104—28no—
645#103—28no—
646#99—28no—
647C24—21no—
648C24—21no—
649C24C2×D4×C13911yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C13914yes—
720C2×Q8C2×D4×C13912yes—
721C2×Q8C2×D4×C13912yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C13912yes—
745C2×D4C2×D4×C13912yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C13911yescharacteristic
770C22×C4C2×D4×C13911yescharacteristic
771C22×C4C2×D4×C13911yescharacteristic
772C22×C4C2×D4×C13911yescharacteristic
773C22×C4C2×D4×C13911yescharacteristic
774C22×C4C2×D4×C13911yescharacteristic
775C22×C4C2×D4×C13911yescharacteristic
776C22×C4C2×D4×C13911yescharacteristic
777C22×C4C2×D4×C13911yescharacteristic
778C22×C4C2×D4×C13911yescharacteristic
779C22×C4C2×D4×C13911yescharacteristic
780C22×C4#41×C13911yescharacteristic
781C22×C4#41×C13911yescharacteristic
782C22×C4C24×C13911yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C13914yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C13914yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C13914yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#120×C13911yescharacteristic
827C23#120×C13911yescharacteristic
828C23#121×C13911yescharacteristic
829C23#121×C13911yescharacteristic
830C23#127×C13911yescharacteristic
831C23#127×C13911yescharacteristic
832C23C22×D4×C13911yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—42no—
844Q8—42no—
845Q8—41no—
846Q8—41no—
847Q8—41no—
848Q8—41no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4#120×C13911yescharacteristic
891C2×C4#120×C13911yescharacteristic
892C2×C4#120×C13911yescharacteristic
893C2×C4#120×C13911yescharacteristic
894C2×C4#120×C13911yescharacteristic
895C2×C4#120×C13911yescharacteristic
896C2×C4#120×C13911yescharacteristic
897C2×C4#120×C13911yescharacteristic
898C2×C4#120×C13911yescharacteristic
899C2×C4#120×C13911yescharacteristic
900C2×C4#121×C13911yescharacteristic
901C2×C4#121×C13911yescharacteristic
902C2×C4#121×C13911yescharacteristic
903C2×C4#121×C13911yescharacteristic
904C2×C4#121×C13911yescharacteristic
905C2×C4#121×C13911yescharacteristic
906C2×C4#121×C13911yescharacteristic
907C2×C4#121×C13911yescharacteristic
908C2×C4#121×C13911yescharacteristic
909C2×C4#121×C13911yescharacteristic
910C2×C4#127×C13911yescharacteristic
911C2×C4#127×C13911yescharacteristic
912C2×C4C22×D4×C13911yescharacteristic
913C2×C4C22×D4×C13911yescharacteristic
914C2×C4C22×D4×C13911yescharacteristic
915C2×C4C22×D4×C13911yescharacteristic
916C2×C4C22×D4×C13911yescharacteristic
917C2×C4C2×#41×C13911yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22#392×C13911yescharacteristic
936C22#392×C13911yescharacteristic
937C22#392×C13911yescharacteristic
938C22#392×C13911yescharacteristic
939C22C2×#120×C13911yescharacteristic
940C22C2×#121×C13911yescharacteristic
941C22C2×#127×C13911yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4#392×C13911yescharacteristic
948C4#392×C13911yescharacteristic
949C4#392×C13911yescharacteristic
950C4#392×C13911yescharacteristic
951C4C2×#120×C13911yescharacteristic
952C4C2×#120×C13911yescharacteristic
953C4C2×#121×C13911yescharacteristic
954C4C2×#121×C13911yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2#2009×C13912yesdirect product factor
964C2C2×#392×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#575×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#137×C139C2semidirect
3. C2×#536×C139C2semidirect
4. C2×#421×C139C2semidirect
5. C2×#419×C139C2semidirect
6. C2×#410×C139C2semidirect
7. #2009×C139C2direct (N × H)
8. C2×#344×C139C2semidirect
23. C2×#137×C139C22semidirect
34. #536×C139C22semidirect
42. #421×C139C22semidirect
45. #419×C139C22semidirect
48. #410×C139C22semidirect
50. #344×C139C22semidirect
480. C2×C139#2009direct (N × H)
482. C2×#2009C139direct (N × H)
483. C139C2×#2009direct (N × H)
485. C22×#137C2×C139semidirect
486. C2×#536C2×C139semidirect
487. C2×#421C2×C139semidirect
488. C2×#419C2×C139semidirect
489. C2×#410C2×C139semidirect
490. #2009C2×C139direct (N × H)
491. C2×#344C2×C139semidirect
506. C2×#137C22×C139semidirect
517. #536C22×C139semidirect
525. #421C22×C139semidirect
528. #419C22×C139semidirect
531. #410C22×C139semidirect
533. #344C22×C139semidirect
963. C2#2009×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#575×C1392
C22×#137×C1392
C2×#536×C1392
C2×#421×C1392
C2×#419×C1392
C2×#410×C1392
#2009×C1392
C2×#344×C1392
C2×#2009139