Finite Group Databasebeta

← C139×#23881 #48018477

Subgroups — C139×#23881 #48018477

Order 35584.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic, complemented
2#3489×C139C211yesmaximal, characteristic, complemented
3C2×#456×C139C211yesmaximal, characteristic, complemented
4C2×#454×C139C211yesmaximal, characteristic, complemented
5#3005×C139C211yesmaximal, characteristic, complemented
6#2432×C139C211yesmaximal, characteristic, complemented
7#2007×C139C211yesmaximal, characteristic, complemented
8#2006×C139C211yesmaximal, characteristic, complemented
9#2005×C139C211yesmaximal, characteristic, complemented
10#2003×C139C211yesmaximal, characteristic, complemented
11#1901×C139C211yesmaximal, characteristic, complemented
12#1883×C139C211yesmaximal, characteristic, complemented
13#1882×C139C211yesmaximal, characteristic, complemented
14#1871×C139C211yesmaximal, characteristic, complemented
15#1789×C139C211yesmaximal, characteristic, complemented
16C2×2−1+4×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×#41×C139C2211yescharacteristic
19#575×C139—24no—
20#575×C139—24no—
21C2×#137×C139—21no—
22C2×#137×C139C2211yescharacteristic
23C2×#137×C139C2211yescharacteristic
24C2×#137×C139C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C139—21no—
26C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
29C2×#135×C139—21no—
30C2×#135×C139—21no—
31C22×M16×C139C2211yescharacteristic
32D4×Q8×C139—21no—
33#548×C139—21no—
34#547×C139—21no—
35#547×C139—22no—
36#546×C139—21no—
37#546×C139—22no—
38#537×C139—21no—
39#537×C139C2211yescharacteristic
40#536×C139—21no—
41#536×C139C2211yescharacteristic
42C2×C4⋊Q8×C139C2211yescharacteristic, complemented
43C2×#124×C139C2211yescharacteristic, complemented
44#525×C139—21no—
45#525×C139C2211yescharacteristic
46C2×C22⋊Q8×C139—21no—
47C2×C22⋊Q8×C139C2211yescharacteristic
48#520×C139C2211yescharacteristic
49#456×C139—24no—
50#454×C139—24no—
51#452×C139—21no—
52#452×C139—21no—
53#449×C139—21no—
54#449×C139—21no—
55C2×#104×C139C2211yescharacteristic
56C2×#104×C139C2211yescharacteristic
57C2×#104×C139C2211yescharacteristic
58C2×#104×C139C2211yescharacteristic
59C2×#104×C139C2211yescharacteristic, complemented
60C2×#104×C139C2211yescharacteristic, complemented
61#419×C139C2211yescharacteristic, complemented
62#418×C139C2211yescharacteristic, complemented
63C2×#101×C139C2211yescharacteristic, complemented
64C2×#101×C139C2211yescharacteristic, complemented
65#407×C139C2211yescharacteristic
66#394×C139—22no—
67#391×C139C2211yescharacteristic, complemented
68#390×C139C2211yescharacteristic, complemented
69#385×C139—22no—
70C4×C22⋊C4×C139C2211yescharacteristic
71#343×C139C2211yescharacteristic, complemented
72#343×C139C2211yescharacteristic, complemented
73#339×C139C2211yescharacteristic, complemented
74#339×C139C2211yescharacteristic, complemented
752−1+4×C139—22no—
762−1+4×C139—22no—
772−1+4×C139—41no—
782−1+4×C139—41no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—22no—
83C2×#41×C139—21no—
84C2×#41×C139—22no—
85C2×#41×C139—22no—
86C2×#41×C139—22no—
87C2×#41×C139—22no—
88C2×#41×C139—21no—
89C2×#41×C139—21no—
90C2×#41×C139—21no—
91C2×#41×C139—21no—
92C2×#41×C139—41no—
93C2×#41×C139—41no—
94C2×#41×C139—41no—
95C2×#41×C139—41no—
96C2×#41×C139D411yescharacteristic
97C2×#41×C139D411yescharacteristic
98C2×#41×C139C2311yescharacteristic
99C2×#41×C139C2311yescharacteristic
100C2×#41×C139C2311yescharacteristic
101C22×Q8×C139—21no—
102C22×Q8×C139—21no—
103C22×Q8×C139D411yescharacteristic
104C22×Q8×C139C2311yescharacteristic
105C22×Q8×C139C2311yescharacteristic
106C22×D4×C139—21no—
107C22×D4×C139—21no—
108C22×D4×C139D411yescharacteristic
109C22×D4×C139C2311yescharacteristic
110C23×C4×C139—21no—
111C23×C4×C139—21no—
112C23×C4×C139C2311yescharacteristic
113#137×C139—28no—
114#137×C139—22no—
115#137×C139—22no—
116#137×C139—22no—
117#137×C139—22no—
118#137×C139—41no—
119#137×C139D414yescomplemented
120AGL(1,ℤ/8)×C139—28no—
121AGL(1,ℤ/8)×C139—22no—
122AGL(1,ℤ/8)×C139—22no—
123AGL(1,ℤ/8)×C139—22no—
124AGL(1,ℤ/8)×C139—22no—
125AGL(1,ℤ/8)×C139—41no—
126AGL(1,ℤ/8)×C139D414yescomplemented
127#135×C139—28no—
128#135×C139—28no—
129C2×Q16×C139—21no—
130C2×Q16×C139—21no—
131C2×Q16×C139—21no—
132C2×SD16×C139—21no—
133C2×SD16×C139—21no—
134C2×SD16×C139—21no—
135C2×SD16×C139—21no—
136C2×SD16×C139—21no—
137C2×SD16×C139—21no—
138C2×D8×C139—21no—
139C2×D8×C139—21no—
140C2×D8×C139—21no—
141C2×M16×C139—21no—
142C2×M16×C139—22no—
143C2×M16×C139—22no—
144C2×M16×C139C2311yescharacteristic
145C2×M16×C139C2311yescharacteristic
146C2×M16×C139C2311yescharacteristic
147C2×M16×C139C2311yescharacteristic
148C22×C8×C139—21no—
149C4⋊Q8×C139—22no—
150C4⋊Q8×C139—21no—
151C4⋊Q8×C139—22no—
152C4⋊Q8×C139—41no—
153#124×C139—22no—
154#124×C139—21no—
155#124×C139—22no—
156#124×C139—41no—
157#123×C139—22no—
158#123×C139—22no—
159#123×C139—22no—
160#123×C139—21no—
161#123×C139—22no—
162C22⋊Q8×C139—22no—
163C22⋊Q8×C139—22no—
164C22⋊Q8×C139—22no—
165C22⋊Q8×C139—21no—
166C22⋊Q8×C139—21no—
167C22⋊Q8×C139—21no—
168C22⋊Q8×C139—21no—
169C22⋊Q8×C139—21no—
170C22⋊Q8×C139—21no—
171C22⋊Q8×C139—21no—
172C22⋊Q8×C139—21no—
173C22⋊Q8×C139D411yescharacteristic
174C22⋊Q8×C139D411yescharacteristic
175#121×C139—22no—
176#121×C139—22no—
177#121×C139—22no—
178#121×C139—21no—
179#121×C139—21no—
180#121×C139—22no—
181#121×C139D411yescharacteristic
182#121×C139D411yescharacteristic
183#120×C139—22no—
184#120×C139—21no—
185C4×Q8×C139—21no—
186C4×D4×C139—22no—
187C4×D4×C139—22no—
188C4×D4×C139—21no—
189C4×D4×C139—22no—
190C4×D4×C139—21no—
191C4×D4×C139—21no—
192#117×C139—21no—
193#117×C139C2311yescharacteristic
194C2×C4⋊C4×C139—22no—
195C2×C4⋊C4×C139—21no—
196C2×C4⋊C4×C139—22no—
197C2×C4⋊C4×C139D412yes—
198C2×C4⋊C4×C139C2311yescharacteristic
199C2×C22⋊C4×C139—22no—
200C2×C22⋊C4×C139—21no—
201C2×C22⋊C4×C139—22no—
202C2×C22⋊C4×C139—22no—
203C2×C22⋊C4×C139D412yes—
204C2×C42×C139C2311yescharacteristic
205C2×C42×C139C2311yescharacteristic
206#104×C139—22no—
207#104×C139—22no—
208#104×C139—22no—
209#104×C139—22no—
210#104×C139—41no—
211#104×C139—41no—
212#103×C139—21no—
213#103×C139—21no—
214#102×C139—21no—
215#102×C139—21no—
216#101×C139—22no—
217#101×C139—22no—
218C22⋊C8×C139—21no—
219C22⋊C8×C139—21no—
220#95×C139—21no—
221#95×C139—22no—
222C24×C139—21no—
223C24×C139—21no—
224C24×C139C2×D411yescharacteristic
225#41×C139—21no—
226#41×C139—21no—
227#41×C139—24no—
228#41×C139—24no—
229#41×C139—22no—
230#41×C139—22no—
231#41×C139—21no—
232#41×C139—21no—
233#41×C139—21no—
234#41×C139—21no—
235#41×C139—21no—
236#41×C139—21no—
237#41×C139—21no—
238#41×C139—21no—
239#41×C139—42no—
240#41×C139—42no—
241#41×C139—41no—
242#41×C139—41no—
243#41×C139—42no—
244#41×C139—42no—
245#41×C139—42no—
246#41×C139—42no—
247#41×C139—42no—
248#41×C139—42no—
249#41×C139—44no—
250#41×C139—44no—
251#41×C139—42no—
252#41×C139—42no—
253#41×C139—42no—
254#41×C139—42no—
255#41×C139—42no—
256#41×C139—42no—
257#41×C139C2×D412yes—
258#41×C139C2×D412yes—
259C2×Q8×C139—22no—
260C2×Q8×C139—21no—
261C2×Q8×C139—21no—
262C2×Q8×C139—21no—
263C2×Q8×C139—21no—
264C2×Q8×C139—21no—
265C2×Q8×C139—21no—
266C2×Q8×C139—21no—
267C2×Q8×C139—21no—
268C2×Q8×C139—22no—
269C2×Q8×C139—21no—
270C2×Q8×C139—21no—
271C2×Q8×C139—21no—
272C2×Q8×C139—21no—
273C2×Q8×C139—41no—
274C2×Q8×C139—42no—
275C2×Q8×C139—42no—
276C2×Q8×C139—42no—
277C2×Q8×C139—42no—
278C2×Q8×C139C2×D411yescharacteristic
279C2×Q8×C139C2×D411yescharacteristic
280C2×Q8×C139C2×D412yes—
281C2×Q8×C139C2×D411yescharacteristic
282C2×D4×C139—21no—
283C2×D4×C139—22no—
284C2×D4×C139—22no—
285C2×D4×C139—21no—
286C2×D4×C139—21no—
287C2×D4×C139—21no—
288C2×D4×C139—21no—
289C2×D4×C139—21no—
290C2×D4×C139—22no—
291C2×D4×C139—21no—
292C2×D4×C139—21no—
293C2×D4×C139—21no—
294C2×D4×C139—21no—
295C2×D4×C139—21no—
296C2×D4×C139—21no—
297C2×D4×C139—21no—
298C2×D4×C139—41no—
299C2×D4×C139—42no—
300C2×D4×C139—42no—
301C2×D4×C139—42no—
302C2×D4×C139—42no—
303C2×D4×C139—41no—
304C2×D4×C139—41no—
305C2×D4×C139C2×D411yescharacteristic
306C2×D4×C139C2×D411yescharacteristic
307C2×D4×C139C2×D412yes—
308C2×D4×C139C2×D411yescharacteristic
309C22×C4×C139—21no—
310C22×C4×C139—21no—
311C22×C4×C139—21no—
312C22×C4×C139—21no—
313C22×C4×C139—21no—
314C22×C4×C139—22no—
315C22×C4×C139—22no—
316C22×C4×C139—21no—
317C22×C4×C139—21no—
318C22×C4×C139—21no—
319C22×C4×C139—22no—
320C22×C4×C139—21no—
321C22×C4×C139—21no—
322C22×C4×C139—21no—
323C22×C4×C139—21no—
324C22×C4×C139—21no—
325C22×C4×C139—42no—
326C22×C4×C139—42no—
327C22×C4×C139—42no—
328C22×C4×C139—42no—
329C22×C4×C139—41no—
330C22×C4×C139—41no—
331C22×C4×C139C2×D412yes—
332C22×C4×C139C2×D411yescharacteristic
333C22×C4×C139C2×D411yescharacteristic
334C22×C4×C139C2×D411yescharacteristic
335C22×C4×C139C2×D411yescharacteristic
336C22×C4×C139C2×D411yescharacteristic
337C22×C4×C139C2×D412yes—
338C22×C4×C139C2411yescharacteristic
339Q16×C139—24no—
340Q16×C139—24no—
341Q16×C139—42no—
342SD16×C139—24no—
343SD16×C139—24no—
344SD16×C139—24no—
345SD16×C139—24no—
346SD16×C139—42no—
347SD16×C139—42no—
348D8×C139—24no—
349D8×C139—24no—
350D8×C139—42no—
351M16×C139—24no—
352M16×C139—21no—
353M16×C139—21no—
354M16×C139—21no—
355M16×C139—21no—
356M16×C139—21no—
357M16×C139—21no—
358M16×C139C2×D412yes—
359M16×C139C2×D412yes—
360C2×C8×C139—24no—
361C2×C8×C139—21no—
362C2×C8×C139—21no—
363C2×C8×C139—21no—
364C2×C8×C139—21no—
365C4⋊C4×C139—22no—
366C4⋊C4×C139—22no—
367C4⋊C4×C139—22no—
368C4⋊C4×C139—22no—
369C4⋊C4×C139—21no—
370C4⋊C4×C139—22no—
371C4⋊C4×C139—22no—
372C4⋊C4×C139—21no—
373C4⋊C4×C139—21no—
374C4⋊C4×C139—21no—
375C4⋊C4×C139—44no—
376C4⋊C4×C139C2×D411yescharacteristic
377C4⋊C4×C139C2×D411yescharacteristic
378C22⋊C4×C139—22no—
379C22⋊C4×C139—22no—
380C22⋊C4×C139—22no—
381C22⋊C4×C139—22no—
382C22⋊C4×C139—22no—
383C22⋊C4×C139—21no—
384C22⋊C4×C139—22no—
385C22⋊C4×C139—22no—
386C22⋊C4×C139—21no—
387C22⋊C4×C139—21no—
388C22⋊C4×C139—21no—
389C22⋊C4×C139—21no—
390C22⋊C4×C139—44no—
391C22⋊C4×C139—44no—
392C22⋊C4×C139—42no—
393C42×C139—22no—
394C42×C139—21no—
395C42×C139—21no—
396C42×C139—21no—
397C42×C139—21no—
398C42×C139—21no—
399C23×C139—21no—
400C23×C139—21no—
401C23×C139—21no—
402C23×C139—21no—
403C23×C139—21no—
404C23×C139—22no—
405C23×C139—41no—
406C23×C139—41no—
407C23×C139—42no—
408C23×C139—42no—
409C23×C139—42no—
410C23×C139—42no—
411C23×C139—41no—
412C23×C139—41no—
413C23×C139—81no—
414C23×C139#12011yescharacteristic
415C23×C139#12011yescharacteristic
416C23×C139C22×D411yescharacteristic
417Q8×C139—21no—
418Q8×C139—21no—
419Q8×C139—22no—
420Q8×C139—21no—
421Q8×C139—21no—
422Q8×C139—22no—
423Q8×C139—21no—
424Q8×C139—42no—
425Q8×C139—44no—
426Q8×C139—41no—
427Q8×C139—41no—
428Q8×C139—41no—
429Q8×C139—41no—
430Q8×C139—41no—
431Q8×C139—41no—
432Q8×C139#12012yes—
433D4×C139—22no—
434D4×C139—22no—
435D4×C139—21no—
436D4×C139—22no—
437D4×C139—21no—
438D4×C139—21no—
439D4×C139—21no—
440D4×C139—22no—
441D4×C139—21no—
442D4×C139—42no—
443D4×C139—42no—
444D4×C139—42no—
445D4×C139—42no—
446D4×C139—44no—
447D4×C139—44no—
448D4×C139—44no—
449D4×C139—41no—
450D4×C139—41no—
451D4×C139—41no—
452D4×C139—41no—
453D4×C139—41no—
454D4×C139—41no—
455D4×C139—81no—
456D4×C139—82no—
457D4×C139#12012yes—
458C2×C4×C139—21no—
459C2×C4×C139—21no—
460C2×C4×C139—21no—
461C2×C4×C139—21no—
462C2×C4×C139—21no—
463C2×C4×C139—21no—
464C2×C4×C139—21no—
465C2×C4×C139—21no—
466C2×C4×C139—21no—
467C2×C4×C139—21no—
468C2×C4×C139—21no—
469C2×C4×C139—22no—
470C2×C4×C139—22no—
471C2×C4×C139—22no—
472C2×C4×C139—21no—
473C2×C4×C139—22no—
474C2×C4×C139—21no—
475C2×C4×C139—21no—
476C2×C4×C139—22no—
477C2×C4×C139—21no—
478C2×C4×C139—22no—
479C2×C4×C139—22no—
480C2×C4×C139—22no—
481C2×C4×C139—42no—
482C2×C4×C139—42no—
483C2×C4×C139—42no—
484C2×C4×C139—44no—
485C2×C4×C139—44no—
486C2×C4×C139—44no—
487C2×C4×C139—41no—
488C2×C4×C139—44no—
489C2×C4×C139—41no—
490C2×C4×C139—41no—
491C2×C4×C139—41no—
492C2×C4×C139—41no—
493C2×C4×C139—41no—
494C2×C4×C139—41no—
495C2×C4×C139—41no—
496C2×C4×C139—42no—
497C2×C4×C139—41no—
498C2×C4×C139—41no—
499C2×C4×C139—41no—
500C2×C4×C139—82no—
501C2×C4×C139#12011yescharacteristic
502C2×C4×C139#12011yescharacteristic
503C2×C4×C139C22×D411yescharacteristic
504C2×C4×C139C22×D411yescharacteristic
505C2×C4×C139C22×D411yescharacteristic
506C2×C4×C139C22×D411yescharacteristic
507C2×C4×C139H(5,𝔽2)11yescharacteristic
508C2×C4×C139H(5,𝔽2)11yescharacteristic
509C8×C139—22no—
510C8×C139—22no—
511C8×C139—41no—
512C8×C139—41no—
513C22×C139—21no—
514C22×C139—21no—
515C22×C139—21no—
516C22×C139—21no—
517C22×C139—22no—
518C22×C139—21no—
519C22×C139—21no—
520C22×C139—21no—
521C22×C139—21no—
522C22×C139—44no—
523C22×C139—41no—
524C22×C139—41no—
525C22×C139—41no—
526C22×C139—41no—
527C22×C139—42no—
528C22×C139—41no—
529C22×C139—41no—
530C22×C139—41no—
531C22×C139—41no—
532C22×C139—81no—
533C22×C139—81no—
534C22×C139—82no—
535C22×C139—84no—
536C22×C139—81no—
537C22×C139—81no—
538C22×C139C2×#12011yescharacteristic
539C22×C139D4211yescharacteristic
540C22×C139D4211yescharacteristic
541C4×C139—21no—
542C4×C139—21no—
543C4×C139—22no—
544C4×C139—42no—
545C4×C139—42no—
546C4×C139—41no—
547C4×C139—42no—
548C4×C139—41no—
549C4×C139—42no—
550C4×C139—41no—
551C4×C139—41no—
552C4×C139—81no—
553C4×C139C2×#12011yescharacteristic
554C4×C139#53411yescharacteristic
555C4×C139D4211yescharacteristic
556C4×C139D4211yescharacteristic
557C2×C139—21no—
558C2×C139—21no—
559C2×C139—41no—
560C2×C139—41no—
561C2×C139—42no—
562C2×C139—81no—
563C2×C139—82no—
564C2×C139—81no—
565C2×C139#240311yescharacteristic
566C2×C139#301811yescharacteristic
567C2×C139#302011yescharacteristic
568#23881C13911yesmaximal, characteristic, direct product factor, Sylow
569C139#2388111yescharacteristic, direct product factor, Sylow
570C2×#575C2×C13911yescharacteristic, complemented
571#3489C2×C13911yescharacteristic, complemented
572C2×#456C2×C13911yescharacteristic, complemented
573C2×#454C2×C13911yescharacteristic, complemented
574#3005C2×C13911yescharacteristic, complemented
575#2432C2×C13911yescharacteristic, complemented
576#2007C2×C13911yescharacteristic, complemented
577#2006C2×C13911yescharacteristic, complemented
578#2005C2×C13911yescharacteristic, complemented
579#2003C2×C13911yescharacteristic, complemented
580#1901C2×C13911yescharacteristic, complemented
581#1883C2×C13911yescharacteristic, complemented
582#1882C2×C13911yescharacteristic, complemented
583#1871C2×C13911yescharacteristic, complemented
584#1789C2×C13911yescharacteristic, complemented
585C2×2−1+4C22×C13911yescharacteristic
586C22×#41C22×C13911yescharacteristic
587C22×#41C22×C13911yescharacteristic
588#575—24no—
589#575—24no—
590C2×#137—21no—
591C2×#137C22×C13911yescharacteristic
592C2×#137C22×C13911yescharacteristic
593C2×#137C22×C13911yescharacteristic, complemented
594C2×AGL(1,ℤ/8)—21no—
595C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
596C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
597C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
598C2×#135—21no—
599C2×#135—21no—
600C22×M16C22×C13911yescharacteristic
601D4×Q8—21no—
602#548—21no—
603#547—21no—
604#547—22no—
605#546—21no—
606#546—22no—
607#537—21no—
608#537C22×C13911yescharacteristic
609#536—21no—
610#536C22×C13911yescharacteristic
611C2×C4⋊Q8C22×C13911yescharacteristic, complemented
612C2×#124C22×C13911yescharacteristic, complemented
613#525—21no—
614#525C22×C13911yescharacteristic
615C2×C22⋊Q8—21no—
616C2×C22⋊Q8C22×C13911yescharacteristic
617#520C22×C13911yescharacteristic
618#456—24no—
619#454—24no—
620#452—21no—
621#452—21no—
622#449—21no—
623#449—21no—
624C2×#104C22×C13911yescharacteristic
625C2×#104C22×C13911yescharacteristic
626C2×#104C22×C13911yescharacteristic
627C2×#104C22×C13911yescharacteristic
628C2×#104C22×C13911yescharacteristic, complemented
629C2×#104C22×C13911yescharacteristic, complemented
630#419C22×C13911yescharacteristic, complemented
631#418C22×C13911yescharacteristic, complemented
632C2×#101C22×C13911yescharacteristic, complemented
633C2×#101C22×C13911yescharacteristic, complemented
634#407C22×C13911yescharacteristic
635#394—22no—
636#391C22×C13911yescharacteristic, complemented
637#390C22×C13911yescharacteristic, complemented
638#385—22no—
639C4×C22⋊C4C22×C13911yescharacteristic
640#343C22×C13911yescharacteristic, complemented
641#343C22×C13911yescharacteristic, complemented
642#339C22×C13911yescharacteristic, complemented
643#339C22×C13911yescharacteristic, complemented
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C13911yescharacteristic
666C2×#41D4×C13911yescharacteristic
667C2×#41C23×C13911yescharacteristic
668C2×#41C23×C13911yescharacteristic
669C2×#41C23×C13911yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C13911yescharacteristic
673C22×Q8C23×C13911yescharacteristic
674C22×Q8C23×C13911yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C13911yescharacteristic
678C22×D4C23×C13911yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C13911yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C13914yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C13914yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C13911yescharacteristic
714C2×M16C23×C13911yescharacteristic
715C2×M16C23×C13911yescharacteristic
716C2×M16C23×C13911yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C13911yescharacteristic
743C22⋊Q8D4×C13911yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C13911yescharacteristic
751#121D4×C13911yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C13911yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C13912yes—
767C2×C4⋊C4C23×C13911yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C13912yes—
773C2×C42C23×C13911yescharacteristic
774C2×C42C23×C13911yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C13911yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C13912yes—
827#41C2×D4×C13912yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C13911yescharacteristic
848C2×Q8C2×D4×C13911yescharacteristic
849C2×Q8C2×D4×C13912yes—
850C2×Q8C2×D4×C13911yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C13911yescharacteristic
875C2×D4C2×D4×C13911yescharacteristic
876C2×D4C2×D4×C13912yes—
877C2×D4C2×D4×C13911yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C13912yes—
901C22×C4C2×D4×C13911yescharacteristic
902C22×C4C2×D4×C13911yescharacteristic
903C22×C4C2×D4×C13911yescharacteristic
904C22×C4C2×D4×C13911yescharacteristic
905C22×C4C2×D4×C13911yescharacteristic
906C22×C4C2×D4×C13912yes—
907C22×C4C24×C13911yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C13912yes—
928M16C2×D4×C13912yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C13911yescharacteristic
946C4⋊C4C2×D4×C13911yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C13911yescharacteristic
984C23#120×C13911yescharacteristic
985C23C22×D4×C13911yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C13912yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—44no—
1015D4—42no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C13912yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C13911yescharacteristic
1071C2×C4#120×C13911yescharacteristic
1072C2×C4C22×D4×C13911yescharacteristic
1073C2×C4C22×D4×C13911yescharacteristic
1074C2×C4C22×D4×C13911yescharacteristic
1075C2×C4C22×D4×C13911yescharacteristic
1076C2×C4H(5,𝔽2)×C13911yescharacteristic
1077C2×C4H(5,𝔽2)×C13911yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C13911yescharacteristic
1108C22D42×C13911yescharacteristic
1109C22D42×C13911yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C13911yescharacteristic
1123C4#534×C13911yescharacteristic
1124C4D42×C13911yescharacteristic
1125C4D42×C13911yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2#2403×C13911yescharacteristic
1135C2#3018×C13911yescharacteristic
1136C2#3020×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
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
1. C2×#575×C139C2semidirect
2. #3489×C139C2semidirect
3. C2×#456×C139C2semidirect
4. C2×#454×C139C2semidirect
5. #3005×C139C2semidirect
6. #2432×C139C2semidirect
7. #2007×C139C2semidirect
8. #2006×C139C2semidirect
9. #2005×C139C2semidirect
10. #2003×C139C2semidirect
11. #1901×C139C2semidirect
12. #1883×C139C2semidirect
13. #1882×C139C2semidirect
14. #1871×C139C2semidirect
15. #1789×C139C2semidirect
24. C2×#137×C139C22semidirect
28. C2×AGL(1,ℤ/8)×C139C22semidirect
42. C2×C4⋊Q8×C139C22semidirect
43. C2×#124×C139C22semidirect
59. C2×#104×C139C22semidirect
60. C2×#104×C139C22semidirect
61. #419×C139C22semidirect
62. #418×C139C22semidirect
63. C2×#101×C139C22semidirect
64. C2×#101×C139C22semidirect
67. #391×C139C22semidirect
68. #390×C139C22semidirect
71. #343×C139C22semidirect
72. #343×C139C22semidirect
73. #339×C139C22semidirect
74. #339×C139C22semidirect
119. #137×C139D4semidirect
126. AGL(1,ℤ/8)×C139D4semidirect
568. #23881C139direct (N × H)
569. C139#23881direct (N × H)
570. C2×#575C2×C139semidirect
571. #3489C2×C139semidirect
572. C2×#456C2×C139semidirect
573. C2×#454C2×C139semidirect
574. #3005C2×C139semidirect
575. #2432C2×C139semidirect
576. #2007C2×C139semidirect
577. #2006C2×C139semidirect
578. #2005C2×C139semidirect
579. #2003C2×C139semidirect
580. #1901C2×C139semidirect
581. #1883C2×C139semidirect
582. #1882C2×C139semidirect
583. #1871C2×C139semidirect
584. #1789C2×C139semidirect
593. C2×#137C22×C139semidirect
597. C2×AGL(1,ℤ/8)C22×C139semidirect
611. C2×C4⋊Q8C22×C139semidirect
612. C2×#124C22×C139semidirect
628. C2×#104C22×C139semidirect
629. C2×#104C22×C139semidirect
630. #419C22×C139semidirect
631. #418C22×C139semidirect
632. C2×#101C22×C139semidirect
633. C2×#101C22×C139semidirect
636. #391C22×C139semidirect
637. #390C22×C139semidirect
640. #343C22×C139semidirect
641. #343C22×C139semidirect
642. #339C22×C139semidirect
643. #339C22×C139semidirect
688. #137D4×C139semidirect
695. AGL(1,ℤ/8)D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1392
#3489×C1392
C2×#456×C1392
C2×#454×C1392
#3005×C1392
#2432×C1392
#2007×C1392
#2006×C1392
#2005×C1392
#2003×C1392
#1901×C1392
#1883×C1392
#1882×C1392
#1871×C1392
#1789×C1392
#23881139