Finite Group Databasebeta

← C139×#24247 #48018843

Subgroups — C139×#24247 #48018843

Order 35584.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C139C211yesmaximal, characteristic
2C2×#464×C139C211yesmaximal, characteristic, complemented
3C2×#452×C139C211yesmaximal, characteristic, complemented
4C2×#450×C139C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C139C211yesmaximal, characteristic, complemented
6#2536×C139C211yesmaximal, characteristic, complemented
7#2035×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#2001×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1958×C139C211yesmaximal, characteristic, complemented
12#1954×C139C211yesmaximal, characteristic, complemented
13#1804×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×Q16×C139C2211yescharacteristic, complemented
19C22×SD16×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21#546×C139—24no—
22#546×C139—24no—
23C2×#124×C139C2211yescharacteristic
24C2×#123×C139—21no—
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×C22⋊Q8×C139C2211yescharacteristic
27C2×C22⋊Q8×C139C2211yescharacteristic, complemented
28C2×#121×C139—21no—
29C2×#121×C139C2211yescharacteristic
30C2×#120×C139—21no—
31C2×C4×Q8×C139C2211yescharacteristic, complemented
32C2×C4×D4×C139C2211yescharacteristic
33C2×C4×D4×C139C2211yescharacteristic
34C22×C22⋊C4×C139—21no—
35#464×C139—24no—
36#452×C139—24no—
37#450×C139—24no—
38C4×SD16×C139—24no—
39C2×#106×C139C2211yescharacteristic, complemented
40C2×C4⋊C8×C139C2211yescharacteristic, complemented
41C2×#103×C139C2211yescharacteristic, complemented
42C2×#103×C139C2211yescharacteristic, complemented
43C2×#103×C139C2211yescharacteristic, complemented
44C2×#103×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic, complemented
54C2×C22⋊C8×C139C2211yescharacteristic, complemented
55C2×C4×C8×C139C2211yescharacteristic, complemented
56#398×C139—21no—
57#394×C139—21no—
58#388×C139—21no—
59#388×C139—21no—
60#382×C139C2211yescharacteristic, complemented
61#380×C139C2211yescharacteristic
62#380×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×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×Q8×C139C2311yescharacteristic
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—22no—
77C22×D4×C139—22no—
78C22×D4×C139—22no—
79C22×D4×C139—22no—
80C22×D4×C139—21no—
81C22×D4×C139—41no—
82C22×D4×C139—41no—
83C22×D4×C139D411yescharacteristic
84C22×D4×C139C2311yescharacteristic
85C22×D4×C139C2311yescharacteristic
86C23×C4×C139—21no—
87C23×C4×C139—21no—
88C23×C4×C139C2311yescharacteristic
89C23×C4×C139C2311yescharacteristic
90C2×Q16×C139—22no—
91C2×Q16×C139—22no—
92C2×Q16×C139—41no—
93C2×SD16×C139—22no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×SD16×C139—41no—
98C2×SD16×C139D414yescomplemented
99C22×C8×C139C2311yescharacteristic
100C22×C8×C139C2311yescharacteristic
101C22×C8×C139C2311yescharacteristic
102C22×C8×C139C2311yescharacteristic
103#124×C139—22no—
104#124×C139D414yes—
105#123×C139—28no—
106C22⋊Q8×C139—22no—
107C22⋊Q8×C139—22no—
108C22⋊Q8×C139—22no—
109C22⋊Q8×C139—22no—
110C22⋊Q8×C139—41no—
111C22⋊Q8×C139—41no—
112#121×C139—28no—
113#121×C139—22no—
114#121×C139—22no—
115#120×C139—28no—
116C4×Q8×C139—22no—
117C4×Q8×C139—22no—
118C4×D4×C139—22no—
119C4×D4×C139—22no—
120C4×D4×C139—22no—
121C4×D4×C139D414yes—
122C2×C4⋊C4×C139—21no—
123C2×C4⋊C4×C139—21no—
124C2×C4⋊C4×C139—21no—
125C2×C4⋊C4×C139—21no—
126C2×C4⋊C4×C139D411yescharacteristic
127C2×C4⋊C4×C139C2311yescharacteristic
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C4⋊C4×C139C2311yescharacteristic
130C2×C4⋊C4×C139C2311yescharacteristic
131C2×C22⋊C4×C139—28no—
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×C139D411yescharacteristic
142C2×C22⋊C4×C139D411yescharacteristic
143C2×C42×C139—21no—
144C2×C42×C139C2311yescharacteristic
145#106×C139—22no—
146C4⋊C8×C139—22no—
147#103×C139—22no—
148#103×C139—22no—
149#103×C139—22no—
150#103×C139—41no—
151#102×C139—22no—
152#102×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—41no—
157C22⋊C8×C139—22no—
158C22⋊C8×C139—22no—
159C22⋊C8×C139—41no—
160C22⋊C8×C139—41no—
161C4×C8×C139—22no—
162#95×C139—21no—
163#95×C139—21no—
164#95×C139—21no—
165#95×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
176C24×C139C2×D411yescharacteristic
177#41×C139—44no—
178#41×C139—44no—
179#41×C139—44no—
180#41×C139—44no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139C2×D412yes—
192C2×Q8×C139C2×D412yes—
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—22no—
196C2×D4×C139—24no—
197C2×D4×C139—22no—
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—41no—
207C2×D4×C139—42no—
208C2×D4×C139—42no—
209C2×D4×C139—44no—
210C2×D4×C139—44no—
211C2×D4×C139—44no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—44no—
215C2×D4×C139—81no—
216C2×D4×C139—81no—
217C2×D4×C139C2×D412yes—
218C2×D4×C139C2×D412yes—
219C2×D4×C139C2×D412yes—
220C2×D4×C139#4112yes—
221C22×C4×C139—24no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
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—24no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—42no—
242C22×C4×C139—42no—
243C22×C4×C139—81no—
244C22×C4×C139—81no—
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D411yescharacteristic
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2411yescharacteristic
250Q16×C139—44no—
251SD16×C139—28no—
252SD16×C139—44no—
253C2×C8×C139—21no—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139C2×D412yes—
265C4⋊C4×C139—24no—
266C4⋊C4×C139—22no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—42no—
275C4⋊C4×C139—42no—
276C4⋊C4×C139—42no—
277C4⋊C4×C139C2×D412yes—
278C22⋊C4×C139—24no—
279C22⋊C4×C139—24no—
280C22⋊C4×C139—22no—
281C22⋊C4×C139—24no—
282C22⋊C4×C139—24no—
283C22⋊C4×C139—24no—
284C22⋊C4×C139—22no—
285C22⋊C4×C139—42no—
286C22⋊C4×C139—42no—
287C22⋊C4×C139—42no—
288C22⋊C4×C139—42no—
289C42×C139—42no—
290C42×C139C2×D412yes—
291C42×C139C2×D412yes—
292C23×C139—21no—
293C23×C139—22no—
294C23×C139—21no—
295C23×C139—22no—
296C23×C139—21no—
297C23×C139—22no—
298C23×C139—21no—
299C23×C139—21no—
300C23×C139—21no—
301C23×C139—22no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—21no—
307C23×C139—21no—
308C23×C139—21no—
309C23×C139—48no—
310C23×C139—48no—
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—84no—
322C23×C139—84no—
323C23×C139—84no—
324C23×C139—84no—
325C23×C139—84no—
326C23×C139#13512yes—
327C23×C139C22×D411yescharacteristic
328Q8×C139—22no—
329Q8×C139—22no—
330Q8×C139—22no—
331Q8×C139—22no—
332Q8×C139—41no—
333Q8×C139—41no—
334Q8×C139—41no—
335Q8×C139—41no—
336D4×C139—22no—
337D4×C139—22no—
338D4×C139—22no—
339D4×C139—22no—
340D4×C139—22no—
341D4×C139—44no—
342D4×C139—48no—
343D4×C139—48no—
344D4×C139—41no—
345D4×C139—41no—
346D4×C139—84no—
347D4×C139#12114yes—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—21no—
352C2×C4×C139—22no—
353C2×C4×C139—21no—
354C2×C4×C139—22no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—48no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—41no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
382C2×C4×C139—41no—
383C2×C4×C139—41no—
384C2×C4×C139—41no—
385C2×C4×C139—84no—
386C2×C4×C139#12012yes—
387C2×C4×C139#12012yes—
388C2×C4×C139C22×D411yescharacteristic
389C2×C4×C139C22×D411yescharacteristic
390C2×C4×C139C22×D411yescharacteristic
391C2×C4×C139C2×#4111yescharacteristic
392C2×C4×C139H(5,𝔽2)11yescharacteristic
393C2×C4×C139H(5,𝔽2)11yescharacteristic
394C8×C139—22no—
395C8×C139—41no—
396C8×C139—41no—
397C8×C139—41no—
398C22×C139—24no—
399C22×C139—22no—
400C22×C139—22no—
401C22×C139—22no—
402C22×C139—41no—
403C22×C139—42no—
404C22×C139—42no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—42no—
408C22×C139—42no—
409C22×C139—42no—
410C22×C139—41no—
411C22×C139—42no—
412C22×C139—41no—
413C22×C139—42no—
414C22×C139—41no—
415C22×C139—42no—
416C22×C139—41no—
417C22×C139—42no—
418C22×C139—41no—
419C22×C139—41no—
420C22×C139—41no—
421C22×C139—41no—
422C22×C139—816no—
423C22×C139—81no—
424C22×C139—81no—
425C22×C139—81no—
426C22×C139—81no—
427C22×C139C2×#12011yescharacteristic
428C22×C139D4211yescharacteristic
429C22×C139#54611yescharacteristic
430C22×C139C2×#13511yescharacteristic
431C22×C139#57511yescharacteristic
432C22×C139#57711yescharacteristic
433C22×C139#57711yescharacteristic
434C4×C139—22no—
435C4×C139—22no—
436C4×C139—41no—
437C4×C139—41no—
438C4×C139—42no—
439C4×C139—42no—
440C4×C139—42no—
441C4×C139—81no—
442C4×C139—81no—
443C4×C139—81no—
444C4×C139C2×#12111yescharacteristic
445C4×C139#53511yescharacteristic
446C4×C139D4211yescharacteristic
447C4×C139#54611yescharacteristic
448C2×C139—42no—
449C2×C139—44no—
450C2×C139—81no—
451C2×C139—82no—
452C2×C139#240811yescharacteristic
453C2×C139#300211yescharacteristic
454C2×C139#300911yescharacteristic
455C2×C139#327511yescharacteristic
456C2×C139#328211yescharacteristic
457C2×C139#329611yescharacteristic
458C2×C139#332311yescharacteristic
459#24247C13911yesmaximal, characteristic, direct product factor, Sylow
460C139#2424711yescharacteristic, direct product factor, Sylow
461C2×#546C2×C13911yescharacteristic
462C2×#464C2×C13911yescharacteristic, complemented
463C2×#452C2×C13911yescharacteristic, complemented
464C2×#450C2×C13911yescharacteristic, complemented
465C2×C4×SD16C2×C13911yescharacteristic, complemented
466#2536C2×C13911yescharacteristic, complemented
467#2035C2×C13911yescharacteristic, complemented
468#2034C2×C13911yescharacteristic, complemented
469#2001C2×C13911yescharacteristic, complemented
470#2000C2×C13911yescharacteristic, complemented
471#1958C2×C13911yescharacteristic, complemented
472#1954C2×C13911yescharacteristic, complemented
473#1804C2×C13911yescharacteristic, complemented
474#1788C2×C13911yescharacteristic, complemented
475#1786C2×C13911yescharacteristic, complemented
476C22×#41C22×C13911yescharacteristic
477C23×D4C22×C13911yescharacteristic
478C22×Q16C22×C13911yescharacteristic, complemented
479C22×SD16C22×C13911yescharacteristic
480C22×SD16C22×C13911yescharacteristic
481#546—24no—
482#546—24no—
483C2×#124C22×C13911yescharacteristic
484C2×#123—21no—
485C2×C22⋊Q8C22×C13911yescharacteristic
486C2×C22⋊Q8C22×C13911yescharacteristic
487C2×C22⋊Q8C22×C13911yescharacteristic, complemented
488C2×#121—21no—
489C2×#121C22×C13911yescharacteristic
490C2×#120—21no—
491C2×C4×Q8C22×C13911yescharacteristic, complemented
492C2×C4×D4C22×C13911yescharacteristic
493C2×C4×D4C22×C13911yescharacteristic
494C22×C22⋊C4—21no—
495#464—24no—
496#452—24no—
497#450—24no—
498C4×SD16—24no—
499C2×#106C22×C13911yescharacteristic, complemented
500C2×C4⋊C8C22×C13911yescharacteristic, complemented
501C2×#103C22×C13911yescharacteristic, complemented
502C2×#103C22×C13911yescharacteristic, complemented
503C2×#103C22×C13911yescharacteristic, complemented
504C2×#103C22×C13911yescharacteristic, complemented
505C2×#102C22×C13911yescharacteristic
506C2×#102C22×C13911yescharacteristic
507C2×#102C22×C13911yescharacteristic
508C2×#102C22×C13911yescharacteristic
509C2×#102C22×C13911yescharacteristic
510C2×#102C22×C13911yescharacteristic
511C2×C22⋊C8C22×C13911yescharacteristic
512C2×C22⋊C8C22×C13911yescharacteristic
513C2×C22⋊C8C22×C13911yescharacteristic, complemented
514C2×C22⋊C8C22×C13911yescharacteristic, complemented
515C2×C4×C8C22×C13911yescharacteristic, complemented
516#398—21no—
517#394—21no—
518#388—21no—
519#388—21no—
520#382C22×C13911yescharacteristic, complemented
521#380C22×C13911yescharacteristic
522#380C22×C13911yescharacteristic, complemented
523#340C22×C13911yescharacteristic, complemented
524#340C22×C13911yescharacteristic, complemented
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C13911yescharacteristic
533C22×Q8C23×C13911yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C13911yescharacteristic
544C22×D4C23×C13911yescharacteristic
545C22×D4C23×C13911yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C13911yescharacteristic
549C23×C4C23×C13911yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C13914yescomplemented
559C22×C8C23×C13911yescharacteristic
560C22×C8C23×C13911yescharacteristic
561C22×C8C23×C13911yescharacteristic
562C22×C8C23×C13911yescharacteristic
563#124—22no—
564#124D4×C13914yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C13914yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C13911yescharacteristic
587C2×C4⋊C4C23×C13911yescharacteristic
588C2×C4⋊C4C23×C13911yescharacteristic
589C2×C4⋊C4C23×C13911yescharacteristic
590C2×C4⋊C4C23×C13911yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C13911yescharacteristic
602C2×C22⋊C4D4×C13911yescharacteristic
603C2×C42—21no—
604C2×C42C23×C13911yescharacteristic
605#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C13911yescharacteristic
636C24C2×D4×C13911yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8C2×D4×C13912yes—
652C2×Q8C2×D4×C13912yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C13912yes—
678C2×D4C2×D4×C13912yes—
679C2×D4C2×D4×C13912yes—
680C2×D4#41×C13912yes—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C13911yescharacteristic
706C22×C4C2×D4×C13911yescharacteristic
707C22×C4C2×D4×C13911yescharacteristic
708C22×C4C2×D4×C13911yescharacteristic
709C22×C4C24×C13911yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×D4×C13912yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C13912yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C13912yes—
751C42C2×D4×C13912yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C13912yes—
787C23C22×D4×C13911yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C13914yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C13912yes—
847C2×C4#120×C13912yes—
848C2×C4C22×D4×C13911yescharacteristic
849C2×C4C22×D4×C13911yescharacteristic
850C2×C4C22×D4×C13911yescharacteristic
851C2×C4C2×#41×C13911yescharacteristic
852C2×C4H(5,𝔽2)×C13911yescharacteristic
853C2×C4H(5,𝔽2)×C13911yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—22no—
859C22—22no—
860C22—24no—
861C22—22no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—42no—
877C22—41no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C13911yescharacteristic
888C22D42×C13911yescharacteristic
889C22#546×C13911yescharacteristic
890C22C2×#135×C13911yescharacteristic
891C22#575×C13911yescharacteristic
892C22#577×C13911yescharacteristic
893C22#577×C13911yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C13911yescharacteristic
905C4#535×C13911yescharacteristic
906C4D42×C13911yescharacteristic
907C4#546×C13911yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2#2408×C13911yescharacteristic
913C2#3002×C13911yescharacteristic
914C2#3009×C13911yescharacteristic
915C2#3275×C13911yescharacteristic
916C2#3282×C13911yescharacteristic
917C2#3296×C13911yescharacteristic
918C2#3323×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#546×C139C2
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
2. C2×#464×C139C2semidirect
3. C2×#452×C139C2semidirect
4. C2×#450×C139C2semidirect
5. C2×C4×SD16×C139C2semidirect
6. #2536×C139C2semidirect
7. #2035×C139C2semidirect
8. #2034×C139C2semidirect
9. #2001×C139C2semidirect
10. #2000×C139C2semidirect
11. #1958×C139C2semidirect
12. #1954×C139C2semidirect
13. #1804×C139C2semidirect
14. #1788×C139C2semidirect
15. #1786×C139C2semidirect
18. C22×Q16×C139C22semidirect
27. C2×C22⋊Q8×C139C22semidirect
31. C2×C4×Q8×C139C22semidirect
39. C2×#106×C139C22semidirect
40. C2×C4⋊C8×C139C22semidirect
41. C2×#103×C139C22semidirect
42. C2×#103×C139C22semidirect
43. C2×#103×C139C22semidirect
44. C2×#103×C139C22semidirect
53. C2×C22⋊C8×C139C22semidirect
54. C2×C22⋊C8×C139C22semidirect
55. C2×C4×C8×C139C22semidirect
60. #382×C139C22semidirect
62. #380×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
98. C2×SD16×C139D4semidirect
459. #24247C139direct (N × H)
460. C139#24247direct (N × H)
462. C2×#464C2×C139semidirect
463. C2×#452C2×C139semidirect
464. C2×#450C2×C139semidirect
465. C2×C4×SD16C2×C139semidirect
466. #2536C2×C139semidirect
467. #2035C2×C139semidirect
468. #2034C2×C139semidirect
469. #2001C2×C139semidirect
470. #2000C2×C139semidirect
471. #1958C2×C139semidirect
472. #1954C2×C139semidirect
473. #1804C2×C139semidirect
474. #1788C2×C139semidirect
475. #1786C2×C139semidirect
478. C22×Q16C22×C139semidirect
487. C2×C22⋊Q8C22×C139semidirect
491. C2×C4×Q8C22×C139semidirect
499. C2×#106C22×C139semidirect
500. C2×C4⋊C8C22×C139semidirect
501. C2×#103C22×C139semidirect
502. C2×#103C22×C139semidirect
503. C2×#103C22×C139semidirect
504. C2×#103C22×C139semidirect
513. C2×C22⋊C8C22×C139semidirect
514. C2×C22⋊C8C22×C139semidirect
515. C2×C4×C8C22×C139semidirect
520. #382C22×C139semidirect
522. #380C22×C139semidirect
523. #340C22×C139semidirect
524. #340C22×C139semidirect
558. C2×SD16D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1392
C2×#464×C1392
C2×#452×C1392
C2×#450×C1392
C2×C4×SD16×C1392
#2536×C1392
#2035×C1392
#2034×C1392
#2001×C1392
#2000×C1392
#1958×C1392
#1954×C1392
#1804×C1392
#1788×C1392
#1786×C1392
#24247139