Finite Group Databasebeta

← C139×#23871 #48018467

Subgroups — C139×#23871 #48018467

Order 35584.

1782 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C211yesmaximal, characteristic, complemented
3C2×#452×C139C211yesmaximal, characteristic, complemented
4C2×#449×C139C211yesmaximal, characteristic, complemented
5C2×#449×C139C211yesmaximal, characteristic, complemented
6#2407×C139C211yesmaximal, characteristic, complemented
7#2015×C139C211yesmaximal, characteristic, complemented
8#2012×C139C211yesmaximal, characteristic, complemented
9#2001×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1880×C139C211yesmaximal, characteristic, complemented
13#1878×C139C211yesmaximal, characteristic, complemented
14#1870×C139C211yesmaximal, characteristic, complemented
15#1787×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C23×Q8×C139C2211yescharacteristic
19C2×#137×C139—24no—
20C2×#137×C139—24no—
21C2×#137×C139—24no—
22C22×Q16×C139C2211yescharacteristic
23C22×Q16×C139C2211yescharacteristic
24C22×SD16×C139C2211yescharacteristic
25C22×SD16×C139C2211yescharacteristic
26C22×SD16×C139C2211yescharacteristic
27C22×D8×C139C2211yescharacteristic
28C22×M16×C139C2211yescharacteristic
29#548×C139—24no—
30#548×C139—24no—
31C2×#124×C139—21no—
32C2×#124×C139C2211yescharacteristic
33C2×C22⋊Q8×C139—21no—
34C2×C22⋊Q8×C139C2211yescharacteristic
35C2×C22⋊Q8×C139C2211yescharacteristic
36C2×#121×C139—21no—
37C2×#121×C139C2211yescharacteristic
38C2×#121×C139C2211yescharacteristic
39C2×C4×Q8×C139C2211yescharacteristic
40C2×C4×D4×C139—21no—
41C2×C4×D4×C139C2211yescharacteristic
42#452×C139—24no—
43#449×C139—24no—
44#449×C139—24no—
45C2×#103×C139C2211yescharacteristic
46C2×#103×C139C2211yescharacteristic
47C2×#103×C139C2211yescharacteristic
48C2×#103×C139C2211yescharacteristic
49C2×#103×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic
51C2×#102×C139C2211yescharacteristic
52C2×#102×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54C2×C22⋊C8×C139C2211yescharacteristic
55C2×C22⋊C8×C139C2211yescharacteristic
56#394×C139—21no—
57#392×C139—21no—
58#391×C139C2211yescharacteristic
59#390×C139C2211yescharacteristic
60#386×C139—21no—
61#385×C139—21no—
62#380×C139C2211yescharacteristic
63#340×C139C2211yescharacteristic
64#340×C139C2211yescharacteristic
65#336×C139C2211yescharacteristic
66#336×C139C2211yescharacteristic
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—22no—
72C2×#41×C139—22no—
73C2×#41×C139—22no—
74C2×#41×C139—22no—
75C2×#41×C139—41no—
76C2×#41×C139—41no—
77C2×#41×C139—41no—
78C2×#41×C139—41no—
79C22×Q8×C139—21no—
80C22×Q8×C139—22no—
81C22×Q8×C139—22no—
82C22×Q8×C139—22no—
83C22×Q8×C139—41no—
84C22×Q8×C139—41no—
85C22×Q8×C139D414yescomplemented
86C22×Q8×C139C2311yescharacteristic
87C22×Q8×C139C2311yescharacteristic
88C22×Q8×C139C2311yescharacteristic
89C22×D4×C139—21no—
90C22×D4×C139—21no—
91C22×D4×C139—21no—
92C22×D4×C139—21no—
93C22×D4×C139D411yescharacteristic
94C22×D4×C139C2311yescharacteristic
95C22×D4×C139C2311yescharacteristic
96C23×C4×C139—21no—
97C23×C4×C139—21no—
98C23×C4×C139—21no—
99C23×C4×C139C2311yescharacteristic
100C23×C4×C139C2311yescharacteristic
101#137×C139—232no—
102C2×Q16×C139—22no—
103C2×Q16×C139—22no—
104C2×Q16×C139—22no—
105C2×Q16×C139—22no—
106C2×Q16×C139—22no—
107C2×Q16×C139D414yescomplemented
108C2×SD16×C139—22no—
109C2×SD16×C139—22no—
110C2×SD16×C139—22no—
111C2×SD16×C139—22no—
112C2×SD16×C139—22no—
113C2×SD16×C139—22no—
114C2×SD16×C139—22no—
115C2×SD16×C139—41no—
116C2×SD16×C139D414yescomplemented
117C2×D8×C139—22no—
118C2×D8×C139—22no—
119C2×D8×C139—41no—
120C2×M16×C139—22no—
121C2×M16×C139—22no—
122C2×M16×C139—22no—
123C22×C8×C139C2311yescharacteristic
124C22×C8×C139C2311yescharacteristic
125C22×C8×C139C2311yescharacteristic
126C22×C8×C139C2311yescharacteristic
127#124×C139—28no—
128#124×C139—22no—
129#124×C139—22no—
130C22⋊Q8×C139—28no—
131C22⋊Q8×C139—22no—
132C22⋊Q8×C139—22no—
133C22⋊Q8×C139—22no—
134C22⋊Q8×C139—41no—
135#121×C139—28no—
136#121×C139—22no—
137#121×C139—22no—
138#121×C139—41no—
139#121×C139D414yescomplemented
140C4×Q8×C139—22no—
141C4×Q8×C139—22no—
142C4×D4×C139—28no—
143C4×D4×C139—22no—
144C4×D4×C139—22no—
145C2×C4⋊C4×C139—21no—
146C2×C4⋊C4×C139—21no—
147C2×C4⋊C4×C139—21no—
148C2×C4⋊C4×C139D411yescharacteristic
149C2×C4⋊C4×C139C2311yescharacteristic
150C2×C4⋊C4×C139C2311yescharacteristic
151C2×C4⋊C4×C139C2311yescharacteristic
152C2×C22⋊C4×C139—21no—
153C2×C22⋊C4×C139—21no—
154C2×C22⋊C4×C139—21no—
155C2×C22⋊C4×C139—21no—
156C2×C22⋊C4×C139—21no—
157C2×C22⋊C4×C139—21no—
158C2×C22⋊C4×C139—21no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—21no—
161C2×C22⋊C4×C139D411yescharacteristic
162C2×C22⋊C4×C139D411yescharacteristic
163C2×C42×C139—21no—
164C2×C42×C139C2311yescharacteristic
165#103×C139—22no—
166#103×C139—22no—
167#103×C139—22no—
168#103×C139—41no—
169#103×C139—41no—
170#102×C139—22no—
171#102×C139—22no—
172#102×C139—22no—
173C22⋊C8×C139—22no—
174C22⋊C8×C139—22no—
175C22⋊C8×C139—22no—
176#95×C139—21no—
177#95×C139—21no—
178#95×C139—21no—
179C24×C139—21no—
180C24×C139—21no—
181C24×C139C2×D411yescharacteristic
182C24×C139C2×D411yescharacteristic
183#41×C139—28no—
184#41×C139—44no—
185#41×C139—44no—
186#41×C139—44no—
187#41×C139—44no—
188#41×C139—44no—
189#41×C139—44no—
190#41×C139—44no—
191C2×Q8×C139—24no—
192C2×Q8×C139—21no—
193C2×Q8×C139—21no—
194C2×Q8×C139—21no—
195C2×Q8×C139—21no—
196C2×Q8×C139—21no—
197C2×Q8×C139—28no—
198C2×Q8×C139—21no—
199C2×Q8×C139—21no—
200C2×Q8×C139—21no—
201C2×Q8×C139—21no—
202C2×Q8×C139—21no—
203C2×Q8×C139—21no—
204C2×Q8×C139—21no—
205C2×Q8×C139—21no—
206C2×Q8×C139—42no—
207C2×Q8×C139—42no—
208C2×Q8×C139—44no—
209C2×Q8×C139—44no—
210C2×Q8×C139—44no—
211C2×Q8×C139C2×D412yes—
212C2×Q8×C139C2×D412yes—
213C2×Q8×C139C2×D412yes—
214C2×Q8×C139C2×D412yes—
215C2×Q8×C139C2×D412yes—
216C2×D4×C139—24no—
217C2×D4×C139—22no—
218C2×D4×C139—24no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—21no—
229C2×D4×C139—41no—
230C2×D4×C139—41no—
231C2×D4×C139—42no—
232C2×D4×C139—42no—
233C2×D4×C139—42no—
234C2×D4×C139—42no—
235C2×D4×C139—42no—
236C2×D4×C139—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—42no—
240C2×D4×C139—81no—
241C2×D4×C139C2×D412yes—
242C2×D4×C139C2×D412yes—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—24no—
249C22×C4×C139—24no—
250C22×C4×C139—21no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—42no—
262C22×C4×C139—42no—
263C22×C4×C139—42no—
264C22×C4×C139—42no—
265C22×C4×C139—42no—
266C22×C4×C139—42no—
267C22×C4×C139—42no—
268C22×C4×C139C2×D411yescharacteristic
269C22×C4×C139C2×D411yescharacteristic
270C22×C4×C139C2×D411yescharacteristic
271C22×C4×C139C2×D411yescharacteristic
272C22×C4×C139C2×D412yes—
273C22×C4×C139C2×D412yes—
274C22×C4×C139C2411yescharacteristic
275Q16×C139—28no—
276Q16×C139—28no—
277SD16×C139—28no—
278SD16×C139—28no—
279SD16×C139—44no—
280D8×C139—44no—
281M16×C139—28no—
282C2×C8×C139—21no—
283C2×C8×C139—21no—
284C2×C8×C139—21no—
285C2×C8×C139—21no—
286C2×C8×C139—21no—
287C2×C8×C139—21no—
288C2×C8×C139—21no—
289C2×C8×C139—21no—
290C2×C8×C139—21no—
291C2×C8×C139—21no—
292C2×C8×C139C2×D412yes—
293C2×C8×C139C2×D412yes—
294C4⋊C4×C139—24no—
295C4⋊C4×C139—24no—
296C4⋊C4×C139—22no—
297C4⋊C4×C139—21no—
298C4⋊C4×C139—21no—
299C4⋊C4×C139—21no—
300C4⋊C4×C139—21no—
301C4⋊C4×C139—21no—
302C4⋊C4×C139—42no—
303C4⋊C4×C139C2×D412yes—
304C22⋊C4×C139—24no—
305C22⋊C4×C139—24no—
306C22⋊C4×C139—24no—
307C22⋊C4×C139—22no—
308C22⋊C4×C139—24no—
309C22⋊C4×C139—22no—
310C22⋊C4×C139—42no—
311C22⋊C4×C139—42no—
312C22⋊C4×C139—42no—
313C22⋊C4×C139—81no—
314C22⋊C4×C139—81no—
315C42×C139—24no—
316C42×C139—21no—
317C42×C139—21no—
318C23×C139—21no—
319C23×C139—21no—
320C23×C139—21no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—21no—
324C23×C139—21no—
325C23×C139—22no—
326C23×C139—21no—
327C23×C139—22no—
328C23×C139—21no—
329C23×C139—21no—
330C23×C139—21no—
331C23×C139—21no—
332C23×C139—21no—
333C23×C139—41no—
334C23×C139—41no—
335C23×C139—41no—
336C23×C139—41no—
337C23×C139—41no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139#12012yes—
346C23×C139C22×D411yescharacteristic
347Q8×C139—22no—
348Q8×C139—22no—
349Q8×C139—22no—
350Q8×C139—22no—
351Q8×C139—22no—
352Q8×C139—22no—
353Q8×C139—22no—
354Q8×C139—48no—
355Q8×C139—41no—
356Q8×C139—41no—
357Q8×C139—41no—
358Q8×C139—41no—
359Q8×C139#12014yes—
360D4×C139—22no—
361D4×C139—22no—
362D4×C139—22no—
363D4×C139—22no—
364D4×C139—48no—
365D4×C139—44no—
366D4×C139—48no—
367D4×C139—48no—
368D4×C139—41no—
369D4×C139—41no—
370D4×C139—41no—
371D4×C139—41no—
372D4×C139—84no—
373C2×C4×C139—22no—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—22no—
377C2×C4×C139—22no—
378C2×C4×C139—22no—
379C2×C4×C139—22no—
380C2×C4×C139—22no—
381C2×C4×C139—22no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—22no—
385C2×C4×C139—22no—
386C2×C4×C139—21no—
387C2×C4×C139—21no—
388C2×C4×C139—22no—
389C2×C4×C139—21no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—48no—
395C2×C4×C139—48no—
396C2×C4×C139—48no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139—41no—
409C2×C4×C139—41no—
410C2×C4×C139—41no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
413C2×C4×C139#12012yes—
414C2×C4×C139C22×D411yescharacteristic
415C2×C4×C139C22×D411yescharacteristic
416C2×C4×C139C22×D411yescharacteristic
417C2×C4×C139C22×D411yescharacteristic
418C2×C4×C139H(5,𝔽2)11yescharacteristic
419C2×C4×C139H(5,𝔽2)11yescharacteristic
420C8×C139—22no—
421C8×C139—22no—
422C8×C139—41no—
423C8×C139—41no—
424C22×C139—22no—
425C22×C139—22no—
426C22×C139—22no—
427C22×C139—41no—
428C22×C139—41no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—42no—
432C22×C139—42no—
433C22×C139—41no—
434C22×C139—41no—
435C22×C139—42no—
436C22×C139—41no—
437C22×C139—42no—
438C22×C139—41no—
439C22×C139—42no—
440C22×C139—41no—
441C22×C139—41no—
442C22×C139—42no—
443C22×C139—41no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139—81no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139—81no—
450C22×C139—81no—
451C22×C139—81no—
452C22×C139C2×#12011yescharacteristic
453C22×C139D4211yescharacteristic
454C22×C139D4211yescharacteristic
455C22×C139#57511yescharacteristic
456C22×C139#57511yescharacteristic
457C22×C139#57711yescharacteristic
458C22×C139#57811yescharacteristic
459C4×C139—22no—
460C4×C139—24no—
461C4×C139—41no—
462C4×C139—42no—
463C4×C139—42no—
464C4×C139—41no—
465C4×C139—42no—
466C4×C139—41no—
467C4×C139—81no—
468C4×C139—81no—
469C4×C139C2×#12011yescharacteristic
470C4×C139#53411yescharacteristic
471C4×C139D4211yescharacteristic
472C4×C139D4211yescharacteristic
473C2×C139—42no—
474C2×C139—81no—
475C2×C139—82no—
476C2×C139—82no—
477C2×C139#240311yescharacteristic
478C2×C139#300511yescharacteristic
479C2×C139#301311yescharacteristic
480C2×C139#326911yescharacteristic
481C2×C139#327111yescharacteristic
482C2×C139#327511yescharacteristic
483C2×C139#327711yescharacteristic
484#23871C13911yesmaximal, characteristic, direct product factor, Sylow
485C139#2387111yescharacteristic, direct product factor, Sylow
486C22×#137C2×C13911yescharacteristic, complemented
487C2×#548C2×C13911yescharacteristic, complemented
488C2×#452C2×C13911yescharacteristic, complemented
489C2×#449C2×C13911yescharacteristic, complemented
490C2×#449C2×C13911yescharacteristic, complemented
491#2407C2×C13911yescharacteristic, complemented
492#2015C2×C13911yescharacteristic, complemented
493#2012C2×C13911yescharacteristic, complemented
494#2001C2×C13911yescharacteristic, complemented
495#2000C2×C13911yescharacteristic, complemented
496#1895C2×C13911yescharacteristic, complemented
497#1880C2×C13911yescharacteristic, complemented
498#1878C2×C13911yescharacteristic, complemented
499#1870C2×C13911yescharacteristic, complemented
500#1787C2×C13911yescharacteristic, complemented
501C22×#41C22×C13911yescharacteristic
502C22×#41C22×C13911yescharacteristic
503C23×Q8C22×C13911yescharacteristic
504C2×#137—24no—
505C2×#137—24no—
506C2×#137—24no—
507C22×Q16C22×C13911yescharacteristic
508C22×Q16C22×C13911yescharacteristic
509C22×SD16C22×C13911yescharacteristic
510C22×SD16C22×C13911yescharacteristic
511C22×SD16C22×C13911yescharacteristic
512C22×D8C22×C13911yescharacteristic
513C22×M16C22×C13911yescharacteristic
514#548—24no—
515#548—24no—
516C2×#124—21no—
517C2×#124C22×C13911yescharacteristic
518C2×C22⋊Q8—21no—
519C2×C22⋊Q8C22×C13911yescharacteristic
520C2×C22⋊Q8C22×C13911yescharacteristic
521C2×#121—21no—
522C2×#121C22×C13911yescharacteristic
523C2×#121C22×C13911yescharacteristic
524C2×C4×Q8C22×C13911yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4C22×C13911yescharacteristic
527#452—24no—
528#449—24no—
529#449—24no—
530C2×#103C22×C13911yescharacteristic
531C2×#103C22×C13911yescharacteristic
532C2×#103C22×C13911yescharacteristic
533C2×#103C22×C13911yescharacteristic
534C2×#103C22×C13911yescharacteristic
535C2×#102C22×C13911yescharacteristic
536C2×#102C22×C13911yescharacteristic
537C2×#102C22×C13911yescharacteristic
538C2×C22⋊C8C22×C13911yescharacteristic
539C2×C22⋊C8C22×C13911yescharacteristic
540C2×C22⋊C8C22×C13911yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C13911yescharacteristic
544#390C22×C13911yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C13911yescharacteristic
548#340C22×C13911yescharacteristic
549#340C22×C13911yescharacteristic
550#336C22×C13911yescharacteristic
551#336C22×C13911yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41—41no—
564C22×Q8—21no—
565C22×Q8—22no—
566C22×Q8—22no—
567C22×Q8—22no—
568C22×Q8—41no—
569C22×Q8—41no—
570C22×Q8D4×C13914yescomplemented
571C22×Q8C23×C13911yescharacteristic
572C22×Q8C23×C13911yescharacteristic
573C22×Q8C23×C13911yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C13911yescharacteristic
579C22×D4C23×C13911yescharacteristic
580C22×D4C23×C13911yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C13911yescharacteristic
585C23×C4C23×C13911yescharacteristic
586#137—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16D4×C13914yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C13914yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—41no—
605C2×M16—22no—
606C2×M16—22no—
607C2×M16—22no—
608C22×C8C23×C13911yescharacteristic
609C22×C8C23×C13911yescharacteristic
610C22×C8C23×C13911yescharacteristic
611C22×C8C23×C13911yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—41no—
620#121—28no—
621#121—22no—
622#121—22no—
623#121—41no—
624#121D4×C13914yescomplemented
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C13911yescharacteristic
634C2×C4⋊C4C23×C13911yescharacteristic
635C2×C4⋊C4C23×C13911yescharacteristic
636C2×C4⋊C4C23×C13911yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C13911yescharacteristic
647C2×C22⋊C4D4×C13911yescharacteristic
648C2×C42—21no—
649C2×C42C23×C13911yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C13911yescharacteristic
667C24C2×D4×C13911yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—28no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C13912yes—
697C2×Q8C2×D4×C13912yes—
698C2×Q8C2×D4×C13912yes—
699C2×Q8C2×D4×C13912yes—
700C2×Q8C2×D4×C13912yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C13912yes—
727C2×D4C2×D4×C13912yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C13911yescharacteristic
754C22×C4C2×D4×C13911yescharacteristic
755C22×C4C2×D4×C13911yescharacteristic
756C22×C4C2×D4×C13911yescharacteristic
757C22×C4C2×D4×C13912yes—
758C22×C4C2×D4×C13912yes—
759C22×C4C24×C13911yescharacteristic
760Q16—28no—
761Q16—28no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—44no—
766M16—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C13912yes—
778C2×C8C2×D4×C13912yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C13912yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—22no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—21no—
812C23—22no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C13912yes—
831C23C22×D4×C13911yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C13914yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C13912yes—
899C2×C4C22×D4×C13911yescharacteristic
900C2×C4C22×D4×C13911yescharacteristic
901C2×C4C22×D4×C13911yescharacteristic
902C2×C4C22×D4×C13911yescharacteristic
903C2×C4H(5,𝔽2)×C13911yescharacteristic
904C2×C4H(5,𝔽2)×C13911yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—42no—
918C22—41no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C13911yescharacteristic
938C22D42×C13911yescharacteristic
939C22D42×C13911yescharacteristic
940C22#575×C13911yescharacteristic
941C22#575×C13911yescharacteristic
942C22#577×C13911yescharacteristic
943C22#578×C13911yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C13911yescharacteristic
955C4#534×C13911yescharacteristic
956C4D42×C13911yescharacteristic
957C4D42×C13911yescharacteristic
958C2—42no—
959C2—81no—
960C2—82no—
961C2—82no—
962C2#2403×C13911yescharacteristic
963C2#3005×C13911yescharacteristic
964C2#3013×C13911yescharacteristic
965C2#3269×C13911yescharacteristic
966C2#3271×C13911yescharacteristic
967C2#3275×C13911yescharacteristic
968C2#3277×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C139C2semidirect
2. C2×#548×C139C2semidirect
3. C2×#452×C139C2semidirect
4. C2×#449×C139C2semidirect
5. C2×#449×C139C2semidirect
6. #2407×C139C2semidirect
7. #2015×C139C2semidirect
8. #2012×C139C2semidirect
9. #2001×C139C2semidirect
10. #2000×C139C2semidirect
11. #1895×C139C2semidirect
12. #1880×C139C2semidirect
13. #1878×C139C2semidirect
14. #1870×C139C2semidirect
15. #1787×C139C2semidirect
85. C22×Q8×C139D4semidirect
107. C2×Q16×C139D4semidirect
116. C2×SD16×C139D4semidirect
139. #121×C139D4semidirect
484. #23871C139direct (N × H)
485. C139#23871direct (N × H)
486. C22×#137C2×C139semidirect
487. C2×#548C2×C139semidirect
488. C2×#452C2×C139semidirect
489. C2×#449C2×C139semidirect
490. C2×#449C2×C139semidirect
491. #2407C2×C139semidirect
492. #2015C2×C139semidirect
493. #2012C2×C139semidirect
494. #2001C2×C139semidirect
495. #2000C2×C139semidirect
496. #1895C2×C139semidirect
497. #1880C2×C139semidirect
498. #1878C2×C139semidirect
499. #1870C2×C139semidirect
500. #1787C2×C139semidirect
570. C22×Q8D4×C139semidirect
592. C2×Q16D4×C139semidirect
601. C2×SD16D4×C139semidirect
624. #121D4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1392
C2×#548×C1392
C2×#452×C1392
C2×#449×C1392
#2407×C1392
#2015×C1392
#2012×C1392
#2001×C1392
#2000×C1392
#1895×C1392
#1880×C1392
#1878×C1392
#1870×C1392
#1787×C1392
#23871139