Finite Group Databasebeta

← C139×#23889 #48018485

Subgroups — C139×#23889 #48018485

Order 35584.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C139C211yesmaximal, characteristic, complemented
2C2×#577×C139C211yesmaximal, characteristic, complemented
3C2×#454×C139C211yesmaximal, characteristic, complemented
4C2×#455×C139C211yesmaximal, characteristic, complemented
5#3013×C139C211yesmaximal, characteristic, complemented
6#3012×C139C211yesmaximal, characteristic, complemented
7#2020×C139C211yesmaximal, characteristic, complemented
8#2019×C139C211yesmaximal, characteristic, complemented
9#2015×C139C211yesmaximal, characteristic, complemented
10#2007×C139C211yesmaximal, characteristic, complemented
11#1908×C139C211yesmaximal, characteristic, complemented
12#1907×C139C211yesmaximal, characteristic, complemented
13#1876×C139C211yesmaximal, characteristic, complemented
14#1876×C139C211yesmaximal, characteristic, complemented
15#1793×C139C211yesmaximal, characteristic, complemented
16C2×2−1+4×C139C2211yescharacteristic
17C2×2−1+4×C139C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C139C2211yescharacteristic
19#578×C139—24no—
20#578×C139—24no—
21#577×C139—24no—
22#577×C139—24no—
23C2×#137×C139—21no—
24C2×#137×C139—21no—
25C2×#137×C139—21no—
26C2×#137×C139C2211yescharacteristic
27C2×#137×C139C2211yescharacteristic
28C2×#137×C139C2211yescharacteristic
29C2×#137×C139C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C139—21no—
31C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
33C2×#135×C139—21no—
34C2×#135×C139—21no—
35C2×#135×C139C2211yescharacteristic
36C2×#135×C139C2211yescharacteristic
37C22×Q16×C139—21no—
38C22×Q16×C139C2211yescharacteristic, complemented
39C22×SD16×C139—21no—
40C22×SD16×C139C2211yescharacteristic
41C2×#131×C139C2211yescharacteristic
42C2×#131×C139C2211yescharacteristic, complemented
43#537×C139C2211yescharacteristic
44C2×#124×C139C2211yescharacteristic
45#455×C139—24no—
46#454×C139—24no—
47#452×C139—21no—
48#452×C139—21no—
49#451×C139—21no—
50#450×C139—21no—
51#449×C139—21no—
52#449×C139—21no—
53#448×C139—21no—
54#447×C139—21no—
55C2×#104×C139C2211yescharacteristic
56C2×#104×C139C2211yescharacteristic
57C2×#104×C139C2211yescharacteristic, complemented
58C2×#104×C139C2211yescharacteristic, complemented
59#417×C139C2211yescharacteristic
60#417×C139C2211yescharacteristic, complemented
61C2×#103×C139C2211yescharacteristic, complemented
62C2×#102×C139C2211yescharacteristic
63C2×#101×C139C2211yescharacteristic, complemented
64C2×#101×C139C2211yescharacteristic, complemented
65C2×#100×C139C2211yescharacteristic
66#408×C139C2211yescharacteristic
67#408×C139C2211yescharacteristic, complemented
68#391×C139C2211yescharacteristic, complemented
69#343×C139C2211yescharacteristic, complemented
70#341×C139C2211yescharacteristic, complemented
71#341×C139C2211yescharacteristic, complemented
72#336×C139C2211yescharacteristic, complemented
732−1+4×C139—22no—
742−1+4×C139—22no—
752−1+4×C139—22no—
762−1+4×C139—22no—
772−1+4×C139—22no—
782−1+4×C139—41no—
792−1+4×C139—41no—
802−1+4×C139D414yescomplemented
81H(5,𝔽2)×C139—22no—
82H(5,𝔽2)×C139—22no—
83H(5,𝔽2)×C139—22no—
84H(5,𝔽2)×C139—41no—
85C2×#41×C139—21no—
86C2×#41×C139—21no—
87C2×#41×C139—21no—
88C2×#41×C139—21no—
89C2×#41×C139—21no—
90C2×#41×C139—21no—
91C2×#41×C139—41no—
92C2×#41×C139—41no—
93C2×#41×C139C2311yescharacteristic
94C2×#41×C139C2311yescharacteristic
95C2×#41×C139C2311yescharacteristic
96C2×#41×C139C2311yescharacteristic
97C22×Q8×C139—21no—
98C22×Q8×C139—21no—
99C22×Q8×C139—21no—
100C22×Q8×C139—21no—
101C22×Q8×C139C2311yescharacteristic
102C22×Q8×C139C2311yescharacteristic
103C22×D4×C139—21no—
104C22×D4×C139—21no—
105C22×D4×C139—41no—
106C22×D4×C139C2311yescharacteristic
107#137×C139—28no—
108#137×C139—28no—
109#137×C139—28no—
110#137×C139—22no—
111#137×C139—22no—
112#137×C139—22no—
113#137×C139—22no—
114#137×C139—22no—
115#137×C139—22no—
116#137×C139—41no—
117#137×C139D414yescomplemented
118AGL(1,ℤ/8)×C139—28no—
119AGL(1,ℤ/8)×C139—22no—
120AGL(1,ℤ/8)×C139—22no—
121AGL(1,ℤ/8)×C139—41no—
122AGL(1,ℤ/8)×C139D414yescomplemented
123#135×C139—28no—
124#135×C139—28no—
125#135×C139—22no—
126#135×C139—22no—
127#135×C139—22no—
128#135×C139—22no—
129C2×Q16×C139—28no—
130C2×Q16×C139—21no—
131C2×Q16×C139—21no—
132C2×Q16×C139—22no—
133C2×Q16×C139—22no—
134C2×Q16×C139—21no—
135C2×Q16×C139—21no—
136C2×Q16×C139—21no—
137C2×Q16×C139—21no—
138C2×Q16×C139D411yescharacteristic
139C2×Q16×C139D411yescharacteristic
140C2×SD16×C139—28no—
141C2×SD16×C139—21no—
142C2×SD16×C139—22no—
143C2×SD16×C139—21no—
144C2×SD16×C139—22no—
145C2×SD16×C139—21no—
146C2×SD16×C139—21no—
147C2×SD16×C139—21no—
148C2×SD16×C139—21no—
149C2×SD16×C139—21no—
150C2×SD16×C139—21no—
151C2×SD16×C139D411yescharacteristic
152C2×SD16×C139D411yescharacteristic
153C2×SD16×C139D411yescharacteristic
154C2×SD16×C139D411yescharacteristic
155C2×D8×C139—21no—
156C2×D8×C139—21no—
157C2×D8×C139D411yescharacteristic
158C2×D8×C139D411yescharacteristic
159#131×C139—22no—
160#131×C139—22no—
161#131×C139—22no—
162#131×C139—22no—
163C2×M16×C139—21no—
164C2×M16×C139—21no—
165C2×M16×C139C2311yescharacteristic
166C2×M16×C139C2311yescharacteristic
167C2×M16×C139C2311yescharacteristic
168C2×M16×C139C2311yescharacteristic
169C22×C8×C139—21no—
170C22×C8×C139—21no—
171C22×C8×C139C2311yescharacteristic
172C22×C8×C139C2311yescharacteristic
173#124×C139—22no—
174#124×C139—22no—
175C22⋊Q8×C139—21no—
176C22⋊Q8×C139—21no—
177#121×C139—21no—
178#121×C139—21no—
179#121×C139—41no—
180C2×C4⋊C4×C139C2311yescharacteristic
181C2×C22⋊C4×C139—41no—
182C2×C42×C139C2311yescharacteristic
183#104×C139—22no—
184#104×C139—22no—
185#104×C139—22no—
186#104×C139—22no—
187#103×C139—21no—
188#103×C139—21no—
189#103×C139—21no—
190#103×C139—21no—
191#102×C139—21no—
192#102×C139—21no—
193#102×C139—21no—
194#102×C139—21no—
195#101×C139—22no—
196#101×C139—41no—
197#100×C139—22no—
198C22⋊C8×C139—21no—
199C22⋊C8×C139—21no—
200C22⋊C8×C139—21no—
201C22⋊C8×C139—21no—
202#95×C139—41no—
203C24×C139—21no—
204C24×C139—41no—
205#41×C139—21no—
206#41×C139—21no—
207#41×C139—21no—
208#41×C139—21no—
209#41×C139—24no—
210#41×C139—24no—
211#41×C139—24no—
212#41×C139—24no—
213#41×C139—21no—
214#41×C139—21no—
215#41×C139—21no—
216#41×C139—21no—
217#41×C139—21no—
218#41×C139—21no—
219#41×C139—21no—
220#41×C139—21no—
221#41×C139—44no—
222#41×C139—42no—
223#41×C139—42no—
224#41×C139—42no—
225#41×C139—44no—
226#41×C139—42no—
227#41×C139—44no—
228#41×C139—42no—
229#41×C139—42no—
230#41×C139—44no—
231#41×C139—42no—
232#41×C139—42no—
233#41×C139C2×D412yes—
234#41×C139C2×D412yes—
235#41×C139C2×D412yes—
236#41×C139C2×D412yes—
237C2×Q8×C139—21no—
238C2×Q8×C139—21no—
239C2×Q8×C139—24no—
240C2×Q8×C139—24no—
241C2×Q8×C139—24no—
242C2×Q8×C139—21no—
243C2×Q8×C139—21no—
244C2×Q8×C139—21no—
245C2×Q8×C139—21no—
246C2×Q8×C139—21no—
247C2×Q8×C139—21no—
248C2×Q8×C139—21no—
249C2×Q8×C139—21no—
250C2×Q8×C139—41no—
251C2×Q8×C139—41no—
252C2×Q8×C139—42no—
253C2×Q8×C139—42no—
254C2×Q8×C139—42no—
255C2×Q8×C139—42no—
256C2×Q8×C139—42no—
257C2×Q8×C139C2×D411yescharacteristic
258C2×Q8×C139C2×D411yescharacteristic
259C2×Q8×C139C2×D412yes—
260C2×Q8×C139C2×D412yes—
261C2×Q8×C139C2×D411yescharacteristic
262C2×Q8×C139C2×D411yescharacteristic
263C2×D4×C139—21no—
264C2×D4×C139—21no—
265C2×D4×C139—24no—
266C2×D4×C139—21no—
267C2×D4×C139—21no—
268C2×D4×C139—21no—
269C2×D4×C139—21no—
270C2×D4×C139—21no—
271C2×D4×C139—21no—
272C2×D4×C139—21no—
273C2×D4×C139—42no—
274C2×D4×C139—41no—
275C2×D4×C139—41no—
276C2×D4×C139—42no—
277C2×D4×C139—44no—
278C2×D4×C139—44no—
279C2×D4×C139—41no—
280C2×D4×C139—41no—
281C2×D4×C139—42no—
282C2×D4×C139—41no—
283C2×D4×C139C2×D411yescharacteristic
284C2×D4×C139C2×D411yescharacteristic
285C2×D4×C139C2×D412yes—
286C2×D4×C139C2×D411yescharacteristic
287C2×D4×C139C2×D411yescharacteristic
288C22×C4×C139—21no—
289C22×C4×C139—21no—
290C22×C4×C139—21no—
291C22×C4×C139—21no—
292C22×C4×C139—21no—
293C22×C4×C139—21no—
294C22×C4×C139—21no—
295C22×C4×C139—21no—
296C22×C4×C139—41no—
297C22×C4×C139—41no—
298C22×C4×C139—41no—
299C22×C4×C139—41no—
300C22×C4×C139—41no—
301C22×C4×C139C2411yescharacteristic
302Q16×C139—24no—
303Q16×C139—24no—
304Q16×C139—24no—
305Q16×C139—24no—
306Q16×C139—22no—
307Q16×C139—24no—
308Q16×C139—22no—
309Q16×C139—42no—
310SD16×C139—24no—
311SD16×C139—24no—
312SD16×C139—24no—
313SD16×C139—24no—
314SD16×C139—22no—
315SD16×C139—24no—
316SD16×C139—22no—
317SD16×C139—24no—
318SD16×C139—22no—
319SD16×C139—22no—
320SD16×C139—42no—
321SD16×C139—42no—
322D8×C139—24no—
323D8×C139—22no—
324D8×C139—22no—
325D8×C139—42no—
326M16×C139—24no—
327M16×C139—24no—
328M16×C139—21no—
329M16×C139—21no—
330M16×C139—21no—
331M16×C139—21no—
332M16×C139—21no—
333M16×C139—21no—
334M16×C139C2×D412yes—
335M16×C139C2×D412yes—
336C2×C8×C139—24no—
337C2×C8×C139—24no—
338C2×C8×C139—21no—
339C2×C8×C139—21no—
340C2×C8×C139—21no—
341C2×C8×C139—21no—
342C2×C8×C139—21no—
343C2×C8×C139—21no—
344C2×C8×C139—21no—
345C2×C8×C139—21no—
346C2×C8×C139C2×D411yescharacteristic
347C2×C8×C139C2×D411yescharacteristic
348C2×C8×C139C2×D411yescharacteristic
349C2×C8×C139C2×D411yescharacteristic
350C4⋊C4×C139—21no—
351C4⋊C4×C139—21no—
352C4⋊C4×C139—41no—
353C22⋊C4×C139—44no—
354C22⋊C4×C139—41no—
355C22⋊C4×C139—41no—
356C42×C139—21no—
357C42×C139—21no—
358C23×C139—21no—
359C23×C139—21no—
360C23×C139—21no—
361C23×C139—21no—
362C23×C139—22no—
363C23×C139—44no—
364C23×C139—41no—
365C23×C139—41no—
366C23×C139—81no—
367C23×C139—81no—
368C23×C139—161no—
369C23×C139—161no—
370C23×C139H(5,𝔽2)11yescharacteristic
371Q8×C139—21no—
372Q8×C139—21no—
373Q8×C139—22no—
374Q8×C139—22no—
375Q8×C139—22no—
376Q8×C139—21no—
377Q8×C139—21no—
378Q8×C139—21no—
379Q8×C139—22no—
380Q8×C139—21no—
381Q8×C139—44no—
382Q8×C139—44no—
383Q8×C139—41no—
384Q8×C139—41no—
385Q8×C139—41no—
386Q8×C139—41no—
387Q8×C139#12012yes—
388Q8×C139#12012yes—
389D4×C139—22no—
390D4×C139—22no—
391D4×C139—22no—
392D4×C139—22no—
393D4×C139—22no—
394D4×C139—21no—
395D4×C139—21no—
396D4×C139—21no—
397D4×C139—21no—
398D4×C139—21no—
399D4×C139—22no—
400D4×C139—21no—
401D4×C139—44no—
402D4×C139—44no—
403D4×C139—44no—
404D4×C139—44no—
405D4×C139—41no—
406D4×C139—41no—
407D4×C139—41no—
408D4×C139—41no—
409D4×C139—41no—
410D4×C139—41no—
411D4×C139—161no—
412D4×C139#12012yes—
413D4×C139#12012yes—
414C2×C4×C139—21no—
415C2×C4×C139—21no—
416C2×C4×C139—22no—
417C2×C4×C139—22no—
418C2×C4×C139—22no—
419C2×C4×C139—22no—
420C2×C4×C139—22no—
421C2×C4×C139—22no—
422C2×C4×C139—21no—
423C2×C4×C139—21no—
424C2×C4×C139—44no—
425C2×C4×C139—44no—
426C2×C4×C139—44no—
427C2×C4×C139—44no—
428C2×C4×C139—44no—
429C2×C4×C139—41no—
430C2×C4×C139—41no—
431C2×C4×C139—41no—
432C2×C4×C139—41no—
433C2×C4×C139—41no—
434C2×C4×C139—41no—
435C2×C4×C139—41no—
436C2×C4×C139—41no—
437C2×C4×C139—41no—
438C2×C4×C139—41no—
439C2×C4×C139—41no—
440C2×C4×C139—41no—
441C2×C4×C139—81no—
442C2×C4×C139C22×D411yescharacteristic
443C2×C4×C139C22×D411yescharacteristic
444C2×C4×C139C22×D411yescharacteristic
445C2×C4×C139C22×D411yescharacteristic
446C2×C4×C139C22×D411yescharacteristic
447C2×C4×C139H(5,𝔽2)11yescharacteristic
448C8×C139—21no—
449C8×C139—21no—
450C8×C139—22no—
451C8×C139—22no—
452C8×C139—21no—
453C8×C139—21no—
454C8×C139—41no—
455C8×C139—41no—
456C22×C139—21no—
457C22×C139—21no—
458C22×C139—22no—
459C22×C139—22no—
460C22×C139—41no—
461C22×C139—41no—
462C22×C139—41no—
463C22×C139—41no—
464C22×C139—41no—
465C22×C139—41no—
466C22×C139—42no—
467C22×C139—41no—
468C22×C139—41no—
469C22×C139—41no—
470C22×C139—41no—
471C22×C139—82no—
472C22×C139—81no—
473C22×C139—81no—
474C22×C139—161no—
475C22×C139—164no—
476C22×C139#53411yescharacteristic
477C22×C139D4211yescharacteristic
478C22×C139D4211yescharacteristic
479C4×C139—22no—
480C4×C139—22no—
481C4×C139—41no—
482C4×C139—42no—
483C4×C139—42no—
484C4×C139—41no—
485C4×C139—81no—
486C4×C139—81no—
487C4×C139C2×#12011yescharacteristic
488C4×C139C2×#12011yescharacteristic
489C4×C139D4211yescharacteristic
490C4×C139D4211yescharacteristic
491C2×C139—21no—
492C2×C139—21no—
493C2×C139—42no—
494C2×C139—42no—
495C2×C139—81no—
496C2×C139—81no—
497C2×C139—82no—
498C2×C139#240311yescharacteristic
499C2×C139#328911yescharacteristic
500C2×C139#329011yescharacteristic
501#23889C13911yesmaximal, characteristic, direct product factor, Sylow
502C139#2388911yescharacteristic, direct product factor, Sylow
503C2×#578C2×C13911yescharacteristic, complemented
504C2×#577C2×C13911yescharacteristic, complemented
505C2×#454C2×C13911yescharacteristic, complemented
506C2×#455C2×C13911yescharacteristic, complemented
507#3013C2×C13911yescharacteristic, complemented
508#3012C2×C13911yescharacteristic, complemented
509#2020C2×C13911yescharacteristic, complemented
510#2019C2×C13911yescharacteristic, complemented
511#2015C2×C13911yescharacteristic, complemented
512#2007C2×C13911yescharacteristic, complemented
513#1908C2×C13911yescharacteristic, complemented
514#1907C2×C13911yescharacteristic, complemented
515#1876C2×C13911yescharacteristic, complemented
516#1876C2×C13911yescharacteristic, complemented
517#1793C2×C13911yescharacteristic, complemented
518C2×2−1+4C22×C13911yescharacteristic
519C2×2−1+4C22×C13911yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C13911yescharacteristic
521#578—24no—
522#578—24no—
523#577—24no—
524#577—24no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137—21no—
528C2×#137C22×C13911yescharacteristic
529C2×#137C22×C13911yescharacteristic
530C2×#137C22×C13911yescharacteristic
531C2×#137C22×C13911yescharacteristic, complemented
532C2×AGL(1,ℤ/8)—21no—
533C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
534C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
535C2×#135—21no—
536C2×#135—21no—
537C2×#135C22×C13911yescharacteristic
538C2×#135C22×C13911yescharacteristic
539C22×Q16—21no—
540C22×Q16C22×C13911yescharacteristic, complemented
541C22×SD16—21no—
542C22×SD16C22×C13911yescharacteristic
543C2×#131C22×C13911yescharacteristic
544C2×#131C22×C13911yescharacteristic, complemented
545#537C22×C13911yescharacteristic
546C2×#124C22×C13911yescharacteristic
547#455—24no—
548#454—24no—
549#452—21no—
550#452—21no—
551#451—21no—
552#450—21no—
553#449—21no—
554#449—21no—
555#448—21no—
556#447—21no—
557C2×#104C22×C13911yescharacteristic
558C2×#104C22×C13911yescharacteristic
559C2×#104C22×C13911yescharacteristic, complemented
560C2×#104C22×C13911yescharacteristic, complemented
561#417C22×C13911yescharacteristic
562#417C22×C13911yescharacteristic, complemented
563C2×#103C22×C13911yescharacteristic, complemented
564C2×#102C22×C13911yescharacteristic
565C2×#101C22×C13911yescharacteristic, complemented
566C2×#101C22×C13911yescharacteristic, complemented
567C2×#100C22×C13911yescharacteristic
568#408C22×C13911yescharacteristic
569#408C22×C13911yescharacteristic, complemented
570#391C22×C13911yescharacteristic, complemented
571#343C22×C13911yescharacteristic, complemented
572#341C22×C13911yescharacteristic, complemented
573#341C22×C13911yescharacteristic, complemented
574#336C22×C13911yescharacteristic, complemented
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C13914yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C13911yescharacteristic
596C2×#41C23×C13911yescharacteristic
597C2×#41C23×C13911yescharacteristic
598C2×#41C23×C13911yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C13911yescharacteristic
604C22×Q8C23×C13911yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C13911yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C13914yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C13914yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C13911yescharacteristic
641C2×Q16D4×C13911yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C13911yescharacteristic
654C2×SD16D4×C13911yescharacteristic
655C2×SD16D4×C13911yescharacteristic
656C2×SD16D4×C13911yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C13911yescharacteristic
660C2×D8D4×C13911yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C13911yescharacteristic
668C2×M16C23×C13911yescharacteristic
669C2×M16C23×C13911yescharacteristic
670C2×M16C23×C13911yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C13911yescharacteristic
674C22×C8C23×C13911yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C13911yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C13911yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C13912yes—
736#41C2×D4×C13912yes—
737#41C2×D4×C13912yes—
738#41C2×D4×C13912yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C13911yescharacteristic
760C2×Q8C2×D4×C13911yescharacteristic
761C2×Q8C2×D4×C13912yes—
762C2×Q8C2×D4×C13912yes—
763C2×Q8C2×D4×C13911yescharacteristic
764C2×Q8C2×D4×C13911yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C13911yescharacteristic
786C2×D4C2×D4×C13911yescharacteristic
787C2×D4C2×D4×C13912yes—
788C2×D4C2×D4×C13911yescharacteristic
789C2×D4C2×D4×C13911yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C13911yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C13912yes—
837M16C2×D4×C13912yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C13911yescharacteristic
849C2×C8C2×D4×C13911yescharacteristic
850C2×C8C2×D4×C13911yescharacteristic
851C2×C8C2×D4×C13911yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C13911yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C13912yes—
890Q8#120×C13912yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C13912yes—
915D4#120×C13912yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C13911yescharacteristic
945C2×C4C22×D4×C13911yescharacteristic
946C2×C4C22×D4×C13911yescharacteristic
947C2×C4C22×D4×C13911yescharacteristic
948C2×C4C22×D4×C13911yescharacteristic
949C2×C4H(5,𝔽2)×C13911yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22#534×C13911yescharacteristic
979C22D42×C13911yescharacteristic
980C22D42×C13911yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C13911yescharacteristic
990C4C2×#120×C13911yescharacteristic
991C4D42×C13911yescharacteristic
992C4D42×C13911yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2#2403×C13911yescharacteristic
1001C2#3289×C13911yescharacteristic
1002C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#578×C139C2semidirect
2. C2×#577×C139C2semidirect
3. C2×#454×C139C2semidirect
4. C2×#455×C139C2semidirect
5. #3013×C139C2semidirect
6. #3012×C139C2semidirect
7. #2020×C139C2semidirect
8. #2019×C139C2semidirect
9. #2015×C139C2semidirect
10. #2007×C139C2semidirect
11. #1908×C139C2semidirect
12. #1907×C139C2semidirect
13. #1876×C139C2semidirect
14. #1876×C139C2semidirect
15. #1793×C139C2semidirect
17. C2×2−1+4×C139C22semidirect
29. C2×#137×C139C22semidirect
38. C22×Q16×C139C22semidirect
42. C2×#131×C139C22semidirect
57. C2×#104×C139C22semidirect
58. C2×#104×C139C22semidirect
60. #417×C139C22semidirect
61. C2×#103×C139C22semidirect
63. C2×#101×C139C22semidirect
64. C2×#101×C139C22semidirect
67. #408×C139C22semidirect
68. #391×C139C22semidirect
69. #343×C139C22semidirect
70. #341×C139C22semidirect
71. #341×C139C22semidirect
72. #336×C139C22semidirect
80. 2−1+4×C139D4semidirect
117. #137×C139D4semidirect
122. AGL(1,ℤ/8)×C139D4semidirect
501. #23889C139direct (N × H)
502. C139#23889direct (N × H)
503. C2×#578C2×C139semidirect
504. C2×#577C2×C139semidirect
505. C2×#454C2×C139semidirect
506. C2×#455C2×C139semidirect
507. #3013C2×C139semidirect
508. #3012C2×C139semidirect
509. #2020C2×C139semidirect
510. #2019C2×C139semidirect
511. #2015C2×C139semidirect
512. #2007C2×C139semidirect
513. #1908C2×C139semidirect
514. #1907C2×C139semidirect
515. #1876C2×C139semidirect
516. #1876C2×C139semidirect
517. #1793C2×C139semidirect
519. C2×2−1+4C22×C139semidirect
531. C2×#137C22×C139semidirect
540. C22×Q16C22×C139semidirect
544. C2×#131C22×C139semidirect
559. C2×#104C22×C139semidirect
560. C2×#104C22×C139semidirect
562. #417C22×C139semidirect
563. C2×#103C22×C139semidirect
565. C2×#101C22×C139semidirect
566. C2×#101C22×C139semidirect
569. #408C22×C139semidirect
570. #391C22×C139semidirect
571. #343C22×C139semidirect
572. #341C22×C139semidirect
573. #341C22×C139semidirect
574. #336C22×C139semidirect
582. 2−1+4D4×C139semidirect
619. #137D4×C139semidirect
624. 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×#578×C1392
C2×#577×C1392
C2×#454×C1392
C2×#455×C1392
#3013×C1392
#3012×C1392
#2020×C1392
#2019×C1392
#2015×C1392
#2007×C1392
#1908×C1392
#1907×C1392
#1876×C1392
#1793×C1392
#23889139