Finite Group Databasebeta

← C139×#24366 #48018962

Subgroups — C139×#24366 #48018962

Order 35584.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
2C2×#463×C139C211yesmaximal, characteristic, complemented
3C2×#459×C139C211yesmaximal, characteristic, complemented
4C2×#447×C139C211yesmaximal, characteristic, complemented
5#2431×C139C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
7#2055×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2012×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1877×C139C211yesmaximal, characteristic, complemented
14#1851×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139—24no—
19C2×AGL(1,ℤ/8)×C139—24no—
20C2×AGL(1,ℤ/8)×C139—24no—
21C22×SD16×C139C2211yescharacteristic
22C22×SD16×C139C2211yescharacteristic
23C22×D8×C139C2211yescharacteristic
24C22×D8×C139C2211yescharacteristic
25C22×D8×C139C2211yescharacteristic
26C22×D8×C139C2211yescharacteristic
27C22×M16×C139C2211yescharacteristic
28C2×#127×C139C2211yescharacteristic, complemented
29C2×#124×C139C2211yescharacteristic, complemented
30C2×#121×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C22×C22⋊C4×C139—21no—
34#463×C139—24no—
35#459×C139—24no—
36#447×C139—24no—
37C2×C4⋊C8×C139C2211yescharacteristic, complemented
38C2×C4⋊C8×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#103×C139C2211yescharacteristic, complemented
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic, complemented
47C2×C22⋊C8×C139C2211yescharacteristic
48#392×C139—21no—
49#392×C139—21no—
50#391×C139C2211yescharacteristic, complemented
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#390×C139C2211yescharacteristic, complemented
54#386×C139—21no—
55#386×C139—21no—
56#386×C139—21no—
57#386×C139—21no—
58#380×C139C2211yescharacteristic
59#379×C139—21no—
60C4×C22⋊C4×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#336×C139C2211yescharacteristic, complemented
64#336×C139C2211yescharacteristic, complemented
65C25×C139—21no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C22×Q8×C139C2311yescharacteristic
73C22×D4×C139—22no—
74C22×D4×C139—22no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—22no—
81C22×D4×C139—41no—
82C22×D4×C139—41no—
83C22×D4×C139D414yescomplemented
84C22×D4×C139C2311yescharacteristic
85C22×D4×C139C2311yescharacteristic
86C22×D4×C139C2311yescharacteristic
87C22×D4×C139C2311yescharacteristic
88C23×C4×C139—21no—
89C23×C4×C139—21no—
90C23×C4×C139—21no—
91C23×C4×C139C2311yescharacteristic
92AGL(1,ℤ/8)×C139—232no—
93C2×SD16×C139—22no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×SD16×C139—22no—
98C2×SD16×C139D414yescomplemented
99C2×D8×C139—22no—
100C2×D8×C139—22no—
101C2×D8×C139—22no—
102C2×D8×C139—22no—
103C2×D8×C139—22no—
104C2×D8×C139—22no—
105C2×D8×C139—22no—
106C2×D8×C139—22no—
107C2×D8×C139—22no—
108C2×D8×C139—41no—
109C2×D8×C139—41no—
110C2×D8×C139D414yescomplemented
111C2×M16×C139—22no—
112C2×M16×C139—22no—
113C2×M16×C139—22no—
114C22×C8×C139C2311yescharacteristic
115C22×C8×C139C2311yescharacteristic
116C22×C8×C139C2311yescharacteristic
117C22×C8×C139C2311yescharacteristic
118#127×C139—22no—
119#127×C139—41no—
120#124×C139—22no—
121#124×C139—41no—
122#121×C139—22no—
123#121×C139—22no—
124C4×D4×C139—22no—
125C4×D4×C139—22no—
126C4×D4×C139—41no—
127C4×D4×C139—41no—
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C4⋊C4×C139C2311yescharacteristic
130C2×C4⋊C4×C139C2311yescharacteristic
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139—21no—
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139—21no—
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—44no—
144C2×C22⋊C4×C139D411yescharacteristic
145C2×C22⋊C4×C139D411yescharacteristic
146C2×C42×C139C2311yescharacteristic
147C2×C42×C139C2311yescharacteristic
148C4⋊C8×C139—22no—
149C4⋊C8×C139—22no—
150#103×C139—22no—
151#103×C139—41no—
152#102×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—22no—
157#102×C139—41no—
158C22⋊C8×C139—22no—
159#95×C139—21no—
160#95×C139—21no—
161#95×C139—21no—
162#95×C139D411yescharacteristic
163#95×C139D411yescharacteristic
164C24×C139—21no—
165C24×C139—21no—
166C24×C139—21no—
167C24×C139—24no—
168C24×C139—21no—
169C24×C139—42no—
170C24×C139—42no—
171C24×C139—42no—
172C24×C139—42no—
173C24×C139—81no—
174C24×C139—81no—
175C24×C139C2×D411yescharacteristic
176#41×C139—28no—
177#41×C139—44no—
178#41×C139—44no—
179#41×C139—44no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139C2×D412yes—
186C2×D4×C139—28no—
187C2×D4×C139—24no—
188C2×D4×C139—21no—
189C2×D4×C139—21no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—44no—
208C2×D4×C139—44no—
209C2×D4×C139—44no—
210C2×D4×C139—42no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—42no—
215C2×D4×C139—42no—
216C2×D4×C139—42no—
217C2×D4×C139—42no—
218C2×D4×C139—42no—
219C2×D4×C139—42no—
220C2×D4×C139—81no—
221C2×D4×C139—81no—
222C2×D4×C139—81no—
223C2×D4×C139—81no—
224C2×D4×C139C2×D412yes—
225C2×D4×C139C2×D412yes—
226C2×D4×C139C2×D412yes—
227C2×D4×C139C2×D412yes—
228C2×D4×C139C2×D412yes—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—42no—
238C22×C4×C139—42no—
239C22×C4×C139—42no—
240C22×C4×C139—42no—
241C22×C4×C139—42no—
242C22×C4×C139—42no—
243C22×C4×C139—42no—
244C22×C4×C139—81no—
245C22×C4×C139—81no—
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D411yescharacteristic
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2×D412yes—
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139#4112yes—
253C22×C4×C139C2411yescharacteristic
254SD16×C139—28no—
255SD16×C139—28no—
256D8×C139—28no—
257D8×C139—28no—
258D8×C139—44no—
259D8×C139—44no—
260M16×C139—28no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—21no—
271C2×C8×C139C2×D412yes—
272C2×C8×C139C2×D412yes—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C22⋊C4×C139—22no—
280C22⋊C4×C139—41no—
281C22⋊C4×C139—42no—
282C22⋊C4×C139—42no—
283C22⋊C4×C139—42no—
284C22⋊C4×C139—42no—
285C22⋊C4×C139—42no—
286C22⋊C4×C139—42no—
287C22⋊C4×C139—42no—
288C22⋊C4×C139—42no—
289C22⋊C4×C139—81no—
290C22⋊C4×C139—81no—
291C22⋊C4×C139—81no—
292C22⋊C4×C139—81no—
293C42×C139—21no—
294C42×C139—21no—
295C42×C139—21no—
296C42×C139—21no—
297C23×C139—22no—
298C23×C139—22no—
299C23×C139—22no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—22no—
307C23×C139—22no—
308C23×C139—48no—
309C23×C139—48no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—41no—
321C23×C139—41no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—41no—
333C23×C139—84no—
334C23×C139—84no—
335C23×C139—84no—
336C23×C139—84no—
337C23×C139—84no—
338C23×C139#12112yes—
339C23×C139C22×D411yescharacteristic
340Q8×C139—22no—
341Q8×C139—22no—
342Q8×C139—41no—
343Q8×C139—41no—
344D4×C139—22no—
345D4×C139—22no—
346D4×C139—22no—
347D4×C139—22no—
348D4×C139—22no—
349D4×C139—22no—
350D4×C139—22no—
351D4×C139—48no—
352D4×C139—48no—
353D4×C139—41no—
354D4×C139—41no—
355D4×C139—41no—
356D4×C139—41no—
357D4×C139—41no—
358D4×C139—41no—
359D4×C139—41no—
360D4×C139—41no—
361D4×C139—84no—
362D4×C139—84no—
363D4×C139—84no—
364D4×C139#12014yes—
365C2×C4×C139—21no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—21no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—21no—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—22no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—21no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—48no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—84no—
396C2×C4×C139—84no—
397C2×C4×C139#12112yes—
398C2×C4×C139AGL(1,ℤ/8)12yescomplemented
399C2×C4×C139C22×D411yescharacteristic
400C2×C4×C139C22×D411yescharacteristic
401C2×C4×C139C22×D411yescharacteristic
402C2×C4×C139C2×#4111yescharacteristic
403C2×C4×C139H(5,𝔽2)11yescharacteristic
404C2×C4×C139H(5,𝔽2)11yescharacteristic
405C8×C139—22no—
406C8×C139—22no—
407C8×C139—41no—
408C8×C139—41no—
409C22×C139—22no—
410C22×C139—24no—
411C22×C139—22no—
412C22×C139—22no—
413C22×C139—42no—
414C22×C139—41no—
415C22×C139—41no—
416C22×C139—42no—
417C22×C139—41no—
418C22×C139—42no—
419C22×C139—42no—
420C22×C139—41no—
421C22×C139—42no—
422C22×C139—42no—
423C22×C139—42no—
424C22×C139—42no—
425C22×C139—42no—
426C22×C139—42no—
427C22×C139—42no—
428C22×C139—42no—
429C22×C139—816no—
430C22×C139—81no—
431C22×C139—81no—
432C22×C139—81no—
433C22×C139—81no—
434C22×C139—81no—
435C22×C139—81no—
436C22×C139—81no—
437C22×C139—81no—
438C22×C139—81no—
439C22×C139—81no—
440C22×C139—81no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—81no—
445C22×C139C2×#12111yescharacteristic
446C22×C139D4211yescharacteristic
447C22×C139D4211yescharacteristic
448C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C139#57511yescharacteristic
450C22×C139#57611yescharacteristic
451C22×C139#57611yescharacteristic
452C4×C139—22no—
453C4×C139—22no—
454C4×C139—42no—
455C4×C139—41no—
456C4×C139—41no—
457C4×C139—41no—
458C4×C139—81no—
459C4×C139—81no—
460C4×C139—81no—
461C4×C139C2×#12011yescharacteristic
462C4×C139#53411yescharacteristic
463C4×C139#54611yescharacteristic
464C4×C139#54611yescharacteristic
465C2×C139—42no—
466C2×C139—44no—
467C2×C139—82no—
468C2×C139—82no—
469C2×C139—161no—
470C2×C139#241011yescharacteristic
471C2×C139#303611yescharacteristic
472C2×C139#304111yescharacteristic
473C2×C139#326411yescharacteristic
474C2×C139#326811yescharacteristic
475C2×C139#327311yescharacteristic
476C2×C139#327411yescharacteristic
477#24366C13911yesmaximal, characteristic, direct product factor, Sylow
478C139#2436611yescharacteristic, direct product factor, Sylow
479C22×AGL(1,ℤ/8)C2×C13911yescharacteristic, complemented
480C2×#463C2×C13911yescharacteristic, complemented
481C2×#459C2×C13911yescharacteristic, complemented
482C2×#447C2×C13911yescharacteristic, complemented
483#2431C2×C13911yescharacteristic, complemented
484D4×C22⋊C4C2×C13911yescharacteristic, complemented
485#2055C2×C13911yescharacteristic, complemented
486#2054C2×C13911yescharacteristic, complemented
487#2012C2×C13911yescharacteristic, complemented
488#2011C2×C13911yescharacteristic, complemented
489#1895C2×C13911yescharacteristic, complemented
490#1879C2×C13911yescharacteristic, complemented
491#1877C2×C13911yescharacteristic, complemented
492#1851C2×C13911yescharacteristic, complemented
493#1788C2×C13911yescharacteristic, complemented
494C22×#41C22×C13911yescharacteristic
495C23×D4C22×C13911yescharacteristic
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C2×AGL(1,ℤ/8)—24no—
499C22×SD16C22×C13911yescharacteristic
500C22×SD16C22×C13911yescharacteristic
501C22×D8C22×C13911yescharacteristic
502C22×D8C22×C13911yescharacteristic
503C22×D8C22×C13911yescharacteristic
504C22×D8C22×C13911yescharacteristic
505C22×M16C22×C13911yescharacteristic
506C2×#127C22×C13911yescharacteristic, complemented
507C2×#124C22×C13911yescharacteristic, complemented
508C2×#121C22×C13911yescharacteristic
509C2×C4×D4C22×C13911yescharacteristic
510C2×C4×D4C22×C13911yescharacteristic
511C22×C22⋊C4—21no—
512#463—24no—
513#459—24no—
514#447—24no—
515C2×C4⋊C8C22×C13911yescharacteristic, complemented
516C2×C4⋊C8C22×C13911yescharacteristic, complemented
517C2×#103C22×C13911yescharacteristic, complemented
518C2×#103C22×C13911yescharacteristic, complemented
519C2×#102C22×C13911yescharacteristic
520C2×#102C22×C13911yescharacteristic
521C2×#102C22×C13911yescharacteristic, complemented
522C2×#102C22×C13911yescharacteristic, complemented
523C2×#102C22×C13911yescharacteristic, complemented
524C2×#102C22×C13911yescharacteristic, complemented
525C2×C22⋊C8C22×C13911yescharacteristic
526#392—21no—
527#392—21no—
528#391C22×C13911yescharacteristic, complemented
529#390C22×C13911yescharacteristic
530#390C22×C13911yescharacteristic
531#390C22×C13911yescharacteristic, complemented
532#386—21no—
533#386—21no—
534#386—21no—
535#386—21no—
536#380C22×C13911yescharacteristic
537#379—21no—
538C4×C22⋊C4C22×C13911yescharacteristic
539#340C22×C13911yescharacteristic, complemented
540#340C22×C13911yescharacteristic, complemented
541#336C22×C13911yescharacteristic, complemented
542#336C22×C13911yescharacteristic, complemented
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C13911yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C13914yescomplemented
562C22×D4C23×C13911yescharacteristic
563C22×D4C23×C13911yescharacteristic
564C22×D4C23×C13911yescharacteristic
565C22×D4C23×C13911yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C13911yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C13914yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C13914yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C13911yescharacteristic
593C22×C8C23×C13911yescharacteristic
594C22×C8C23×C13911yescharacteristic
595C22×C8C23×C13911yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C13911yescharacteristic
607C2×C4⋊C4C23×C13911yescharacteristic
608C2×C4⋊C4C23×C13911yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C13911yescharacteristic
623C2×C22⋊C4D4×C13911yescharacteristic
624C2×C42C23×C13911yescharacteristic
625C2×C42C23×C13911yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C13911yescharacteristic
641#95D4×C13911yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C13911yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C13912yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C13912yes—
703C2×D4C2×D4×C13912yes—
704C2×D4C2×D4×C13912yes—
705C2×D4C2×D4×C13912yes—
706C2×D4C2×D4×C13912yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C13911yescharacteristic
725C22×C4C2×D4×C13911yescharacteristic
726C22×C4C2×D4×C13911yescharacteristic
727C22×C4C2×D4×C13911yescharacteristic
728C22×C4C2×D4×C13912yes—
729C22×C4C2×D4×C13911yescharacteristic
730C22×C4#41×C13912yes—
731C22×C4C24×C13911yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C13912yes—
750C2×C8C2×D4×C13912yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C13912yes—
817C23C22×D4×C13911yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C13914yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4—84no—
875C2×C4#121×C13912yes—
876C2×C4AGL(1,ℤ/8)×C13912yescomplemented
877C2×C4C22×D4×C13911yescharacteristic
878C2×C4C22×D4×C13911yescharacteristic
879C2×C4C22×D4×C13911yescharacteristic
880C2×C4C2×#41×C13911yescharacteristic
881C2×C4H(5,𝔽2)×C13911yescharacteristic
882C2×C4H(5,𝔽2)×C13911yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C13911yescharacteristic
924C22D42×C13911yescharacteristic
925C22D42×C13911yescharacteristic
926C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
927C22#575×C13911yescharacteristic
928C22#576×C13911yescharacteristic
929C22#576×C13911yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C13911yescharacteristic
940C4#534×C13911yescharacteristic
941C4#546×C13911yescharacteristic
942C4#546×C13911yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2#2410×C13911yescharacteristic
949C2#3036×C13911yescharacteristic
950C2#3041×C13911yescharacteristic
951C2#3264×C13911yescharacteristic
952C2#3268×C13911yescharacteristic
953C2#3273×C13911yescharacteristic
954C2#3274×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C139C2semidirect
2. C2×#463×C139C2semidirect
3. C2×#459×C139C2semidirect
4. C2×#447×C139C2semidirect
5. #2431×C139C2semidirect
6. D4×C22⋊C4×C139C2semidirect
7. #2055×C139C2semidirect
8. #2054×C139C2semidirect
9. #2012×C139C2semidirect
10. #2011×C139C2semidirect
11. #1895×C139C2semidirect
12. #1879×C139C2semidirect
13. #1877×C139C2semidirect
14. #1851×C139C2semidirect
15. #1788×C139C2semidirect
28. C2×#127×C139C22semidirect
29. C2×#124×C139C22semidirect
37. C2×C4⋊C8×C139C22semidirect
38. C2×C4⋊C8×C139C22semidirect
39. C2×#103×C139C22semidirect
40. C2×#103×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
46. C2×#102×C139C22semidirect
50. #391×C139C22semidirect
53. #390×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #336×C139C22semidirect
64. #336×C139C22semidirect
83. C22×D4×C139D4semidirect
98. C2×SD16×C139D4semidirect
110. C2×D8×C139D4semidirect
398. C2×C4×C139AGL(1,ℤ/8)semidirect
477. #24366C139direct (N × H)
478. C139#24366direct (N × H)
479. C22×AGL(1,ℤ/8)C2×C139semidirect
480. C2×#463C2×C139semidirect
481. C2×#459C2×C139semidirect
482. C2×#447C2×C139semidirect
483. #2431C2×C139semidirect
484. D4×C22⋊C4C2×C139semidirect
485. #2055C2×C139semidirect
486. #2054C2×C139semidirect
487. #2012C2×C139semidirect
488. #2011C2×C139semidirect
489. #1895C2×C139semidirect
490. #1879C2×C139semidirect
491. #1877C2×C139semidirect
492. #1851C2×C139semidirect
493. #1788C2×C139semidirect
506. C2×#127C22×C139semidirect
507. C2×#124C22×C139semidirect
515. C2×C4⋊C8C22×C139semidirect
516. C2×C4⋊C8C22×C139semidirect
517. C2×#103C22×C139semidirect
518. C2×#103C22×C139semidirect
521. C2×#102C22×C139semidirect
522. C2×#102C22×C139semidirect
523. C2×#102C22×C139semidirect
524. C2×#102C22×C139semidirect
528. #391C22×C139semidirect
531. #390C22×C139semidirect
539. #340C22×C139semidirect
540. #340C22×C139semidirect
541. #336C22×C139semidirect
542. #336C22×C139semidirect
561. C22×D4D4×C139semidirect
576. C2×SD16D4×C139semidirect
588. C2×D8D4×C139semidirect
876. C2×C4AGL(1,ℤ/8)×C139semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1392
C2×#463×C1392
C2×#459×C1392
C2×#447×C1392
#2431×C1392
D4×C22⋊C4×C1392
#2055×C1392
#2054×C1392
#2012×C1392
#2011×C1392
#1895×C1392
#1879×C1392
#1877×C1392
#1851×C1392
#1788×C1392
#24366139