Finite Group Databasebeta

← C139×#22419 #48017015

Subgroups — C139×#22419 #48017015

Order 35584.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C139C211yesmaximal, characteristic
2C2×#435×C139C211yesmaximal, characteristic, complemented
3C2×#417×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C139C211yesmaximal, characteristic, complemented
6#1983×C139C211yesmaximal, characteristic, complemented
7#1959×C139C211yesmaximal, characteristic, complemented
8#1895×C139C211yesmaximal, characteristic, complemented
9#1892×C139C211yesmaximal, characteristic, complemented
10#1874×C139C211yesmaximal, characteristic, complemented
11#1872×C139C211yesmaximal, characteristic, complemented
12#1802×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic, complemented
19C23×C8×C139C2211yescharacteristic
20#546×C139—24no—
21#546×C139C418yescomplemented
22C2×#124×C139C2211yescharacteristic
23C2×#123×C139—21no—
24C2×C22⋊Q8×C139C2211yescharacteristic
25C2×#121×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#120×C139—21no—
28C2×C4×D4×C139—21no—
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C22×C4⋊C4×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2211yescharacteristic, complemented
33C22×C22⋊C4×C139—21no—
34#435×C139—24no—
35C2×C4⋊C8×C139C2211yescharacteristic, complemented
36#417×C139—24no—
37C2×#103×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#103×C139C2211yescharacteristic, complemented
41C2×#102×C139—24no—
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic, complemented
52C2×#97×C139C2211yescharacteristic, complemented
53#389×C139—21no—
54#385×C139—21no—
55#385×C139—21no—
56#384×C139C2211yescharacteristic, complemented
57#380×C139C2211yescharacteristic
58#380×C139C2211yescharacteristic, complemented
59C4×C4⋊C4×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64C25×C139—21no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C2×#41×C139C2×C414yescomplemented
71C22×Q8×C139C2311yescharacteristic
72C22×D4×C139—22no—
73C22×D4×C139—22no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—22no—
78C22×D4×C139—41no—
79C22×D4×C139—41no—
80C22×D4×C139C2×C414yescomplemented
81C22×D4×C139D411yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2311yescharacteristic
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139—21no—
87C23×C4×C139—21no—
88C23×C4×C139C2311yescharacteristic
89C23×C4×C139C2311yescharacteristic
90C2×M16×C139—22no—
91C2×M16×C139—22no—
92C2×M16×C139—41no—
93C22×C8×C139—22no—
94C22×C8×C139—22no—
95C22×C8×C139—41no—
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99C22×C8×C139C2311yescharacteristic
100#124×C139—22no—
101#124×C139C2×C414yescomplemented
102#123×C139—28no—
103C22⋊Q8×C139—22no—
104C22⋊Q8×C139C2×C414yescomplemented
105#121×C139—22no—
106#121×C139—28no—
107#121×C139C2×C414yescomplemented
108#120×C139—28no—
109C4×D4×C139—22no—
110C4×D4×C139—44no—
111C4×D4×C139C2×C414yes—
112C4×D4×C139C2×C414yescomplemented
113C4×D4×C139D414yes—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—22no—
116C2×C4⋊C4×C139—22no—
117C2×C4⋊C4×C139—21no—
118C2×C4⋊C4×C139—21no—
119C2×C4⋊C4×C139—21no—
120C2×C4⋊C4×C139—21no—
121C2×C4⋊C4×C139—41no—
122C2×C4⋊C4×C139—41no—
123C2×C4⋊C4×C139D411yescharacteristic
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C4⋊C4×C139C2311yescharacteristic
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—28no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139—21no—
137C2×C22⋊C4×C139D411yescharacteristic
138C2×C22⋊C4×C139D411yescharacteristic
139C2×C42×C139—21no—
140C2×C42×C139C2311yescharacteristic
141C4⋊C8×C139—22no—
142#103×C139—22no—
143#103×C139—22no—
144#103×C139—41no—
145#103×C139—41no—
146#102×C139—22no—
147#102×C139—22no—
148#102×C139—22no—
149#102×C139—22no—
150#102×C139—22no—
151#102×C139—41no—
152#102×C139—41no—
153#102×C139D414yescomplemented
154C22⋊C8×C139—22no—
155C22⋊C8×C139—22no—
156#97×C139—22no—
157#95×C139—21no—
158#95×C139—21no—
159#95×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—24no—
163C24×C139—42no—
164C24×C139—42no—
165C24×C139—42no—
166C24×C139—42no—
167C24×C139—81no—
168C24×C139—81no—
169C24×C139C2×D411yescharacteristic
170C24×C139C2×D411yescharacteristic
171#41×C139—28no—
172#41×C139—44no—
173#41×C139—44no—
174#41×C139—44no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139C22×C412yes—
181C2×D4×C139—22no—
182C2×D4×C139—22no—
183C2×D4×C139—28no—
184C2×D4×C139—24no—
185C2×D4×C139—24no—
186C2×D4×C139—24no—
187C2×D4×C139—21no—
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—44no—
196C2×D4×C139—44no—
197C2×D4×C139—44no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—42no—
202C2×D4×C139—81no—
203C2×D4×C139—81no—
204C2×D4×C139C22⋊C414yes—
205C2×D4×C139C22×C412yes—
206C2×D4×C139C22×C412yes—
207C2×D4×C139C2×D412yes—
208C2×D4×C139#4112yes—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—24no—
221C22×C4×C139—24no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—42no—
226C22×C4×C139—42no—
227C22×C4×C139—42no—
228C22×C4×C139—42no—
229C22×C4×C139—42no—
230C22×C4×C139—42no—
231C22×C4×C139—81no—
232C22×C4×C139—81no—
233C22×C4×C139—81no—
234C22×C4×C139—81no—
235C22×C4×C139C22×C412yes—
236C22×C4×C139C22×C412yes—
237C22×C4×C139C2×D411yescharacteristic
238C22×C4×C139C2×D411yescharacteristic
239C22×C4×C139C2×D411yescharacteristic
240C22×C4×C139C2×D411yescharacteristic
241C22×C4×C139C2×D412yes—
242C22×C4×C139C2×D412yes—
243C22×C4×C139C2411yescharacteristic
244M16×C139—44no—
245C2×C8×C139—21no—
246C2×C8×C139—21no—
247C2×C8×C139—21no—
248C2×C8×C139—21no—
249C2×C8×C139—21no—
250C2×C8×C139—21no—
251C2×C8×C139—21no—
252C2×C8×C139—21no—
253C2×C8×C139—21no—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—44no—
257C2×C8×C139C2×D412yes—
258C4⋊C4×C139—24no—
259C4⋊C4×C139—21no—
260C4⋊C4×C139—21no—
261C4⋊C4×C139—21no—
262C4⋊C4×C139—21no—
263C4⋊C4×C139—21no—
264C4⋊C4×C139—21no—
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—42no—
268C4⋊C4×C139—42no—
269C4⋊C4×C139—42no—
270C4⋊C4×C139—81no—
271C4⋊C4×C139C22⋊C414yes—
272C4⋊C4×C139C22×C412yes—
273C4⋊C4×C139C2×D412yes—
274C22⋊C4×C139—24no—
275C22⋊C4×C139—24no—
276C22⋊C4×C139—24no—
277C22⋊C4×C139—24no—
278C22⋊C4×C139—24no—
279C22⋊C4×C139—42no—
280C22⋊C4×C139—42no—
281C22⋊C4×C139C22⋊C414yes—
282C22⋊C4×C139C22⋊C414yes—
283C42×C139—42no—
284C42×C139C22×C412yes—
285C42×C139C2×D412yes—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—22no—
291C23×C139—21no—
292C23×C139—22no—
293C23×C139—21no—
294C23×C139—22no—
295C23×C139—21no—
296C23×C139—21no—
297C23×C139—21no—
298C23×C139—21no—
299C23×C139—22no—
300C23×C139—48no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—48no—
312C23×C139—84no—
313C23×C139—84no—
314C23×C139—84no—
315C23×C139—84no—
316C23×C139—84no—
317C23×C139C2×C22⋊C412yes—
318C23×C139C2×C22⋊C412yes—
319C23×C139AGL(1,ℤ/8)12yes—
320C23×C139#13712yes—
321C23×C139C22×D411yescharacteristic
322Q8×C139—22no—
323Q8×C139—22no—
324Q8×C139—41no—
325Q8×C139—41no—
326D4×C139—28no—
327D4×C139—22no—
328D4×C139—22no—
329D4×C139—22no—
330D4×C139—22no—
331D4×C139—22no—
332D4×C139—48no—
333D4×C139—48no—
334D4×C139—41no—
335D4×C139—41no—
336D4×C139—84no—
337D4×C139C4×D414yescomplemented
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—22no—
347C2×C4×C139—22no—
348C2×C4×C139—22no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
351C2×C4×C139—22no—
352C2×C4×C139—22no—
353C2×C4×C139—22no—
354C2×C4×C139—22no—
355C2×C4×C139—22no—
356C2×C4×C139—22no—
357C2×C4×C139—48no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
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—84no—
374C2×C4×C139—84no—
375C2×C4×C139—84no—
376C2×C4×C139C2×C22⋊C412yes—
377C2×C4×C139C2×C22⋊C412yes—
378C2×C4×C139C2×C22⋊C412yes—
379C2×C4×C139C2×C22⋊C412yes—
380C2×C4×C139C23×C411yescharacteristic
381C2×C4×C139C22×D411yescharacteristic
382C2×C4×C139C22×D411yescharacteristic
383C2×C4×C139C2×#4111yescharacteristic
384C2×C4×C139H(5,𝔽2)11yescharacteristic
385C2×C4×C139H(5,𝔽2)11yescharacteristic
386C8×C139—22no—
387C8×C139—41no—
388C8×C139—41no—
389C8×C139—41no—
390C22×C139—22no—
391C22×C139—22no—
392C22×C139—22no—
393C22×C139—22no—
394C22×C139—22no—
395C22×C139—22no—
396C22×C139—22no—
397C22×C139—24no—
398C22×C139—22no—
399C22×C139—22no—
400C22×C139—42no—
401C22×C139—42no—
402C22×C139—41no—
403C22×C139—42no—
404C22×C139—41no—
405C22×C139—42no—
406C22×C139—41no—
407C22×C139—42no—
408C22×C139—41no—
409C22×C139—42no—
410C22×C139—42no—
411C22×C139—42no—
412C22×C139—42no—
413C22×C139—816no—
414C22×C139—81no—
415C22×C139—81no—
416C22×C139—81no—
417C22×C139—81no—
418C22×C139#41714yescomplemented
419C22×C139C22×C22⋊C411yescharacteristic
420C22×C139D4211yescharacteristic
421C22×C139#54611yescharacteristic
422C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C139C2×#13711yescharacteristic
424C22×C139#57611yescharacteristic
425C22×C139#57711yescharacteristic
426C4×C139—22no—
427C4×C139—22no—
428C4×C139—22no—
429C4×C139—22no—
430C4×C139—42no—
431C4×C139—42no—
432C4×C139—42no—
433C4×C139—81no—
434C4×C139—81no—
435C4×C139—81no—
436C4×C139C2×C4×D411yescharacteristic
437C4×C139#51811yescharacteristic
438C4×C139D4211yescharacteristic
439C4×C139#54611yescharacteristic
440C2×C139—24no—
441C2×C139—42no—
442C2×C139—44no—
443C2×C139—82no—
444C2×C139D4×C22⋊C411yescharacteristic
445C2×C139C2×#41711yescharacteristic
446C2×C139#289711yescharacteristic
447C2×C139#326411yescharacteristic
448C2×C139#326611yescharacteristic
449C2×C139#330611yescharacteristic
450C2×C139#331411yescharacteristic
451#22419C13911yesmaximal, characteristic, direct product factor, Sylow
452C139#2241911yescharacteristic, direct product factor, Sylow
453C2×#546C2×C13911yescharacteristic
454C2×#435C2×C13911yescharacteristic, complemented
455C2×#417C2×C13911yescharacteristic, complemented
456C22×#102C2×C13911yescharacteristic, complemented
457D4×C4⋊C4C2×C13911yescharacteristic, complemented
458#1983C2×C13911yescharacteristic, complemented
459#1959C2×C13911yescharacteristic, complemented
460#1895C2×C13911yescharacteristic, complemented
461#1892C2×C13911yescharacteristic, complemented
462#1874C2×C13911yescharacteristic, complemented
463#1872C2×C13911yescharacteristic, complemented
464#1802C2×C13911yescharacteristic, complemented
465#1788C2×C13911yescharacteristic, complemented
466#1786C2×C13911yescharacteristic, complemented
467#1762C2×C13911yescharacteristic, complemented
468C22×#41C22×C13911yescharacteristic
469C23×D4C22×C13911yescharacteristic
470C22×M16C22×C13911yescharacteristic, complemented
471C23×C8C22×C13911yescharacteristic
472#546—24no—
473#546C4×C13918yescomplemented
474C2×#124C22×C13911yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C13911yescharacteristic
477C2×#121—21no—
478C2×#121C22×C13911yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C13911yescharacteristic
482C2×C4×D4C22×C13911yescharacteristic
483C22×C4⋊C4C22×C13911yescharacteristic
484C22×C4⋊C4C22×C13911yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C13911yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C13911yescharacteristic, complemented
490C2×#103C22×C13911yescharacteristic, complemented
491C2×#103C22×C13911yescharacteristic, complemented
492C2×#103C22×C13911yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C13911yescharacteristic
495C2×#102C22×C13911yescharacteristic
496C2×#102C22×C13911yescharacteristic
497C2×#102C22×C13911yescharacteristic
498C2×#102C22×C13911yescharacteristic
499C2×#102C22×C13911yescharacteristic
500C2×#102C22×C13911yescharacteristic
501C2×#102C22×C13911yescharacteristic
502C2×C22⋊C8C22×C13911yescharacteristic
503C2×C22⋊C8C22×C13911yescharacteristic, complemented
504C2×#97C22×C13911yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C13911yescharacteristic, complemented
509#380C22×C13911yescharacteristic
510#380C22×C13911yescharacteristic, complemented
511C4×C4⋊C4C22×C13911yescharacteristic, complemented
512#340C22×C13911yescharacteristic, complemented
513#340C22×C13911yescharacteristic, complemented
514#340C22×C13911yescharacteristic, complemented
515#340C22×C13911yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C13914yescomplemented
523C22×Q8C23×C13911yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C13914yescomplemented
533C22×D4D4×C13911yescharacteristic
534C22×D4C23×C13911yescharacteristic
535C22×D4C23×C13911yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C13911yescharacteristic
541C23×C4C23×C13911yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C13911yescharacteristic
549C22×C8C23×C13911yescharacteristic
550C22×C8C23×C13911yescharacteristic
551C22×C8C23×C13911yescharacteristic
552#124—22no—
553#124C2×C4×C13914yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C13914yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C13914yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C13914yes—
564C4×D4C2×C4×C13914yescomplemented
565C4×D4D4×C13914yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C13911yescharacteristic
576C2×C4⋊C4C23×C13911yescharacteristic
577C2×C4⋊C4C23×C13911yescharacteristic
578C2×C4⋊C4C23×C13911yescharacteristic
579C2×C4⋊C4C23×C13911yescharacteristic
580C2×C4⋊C4C23×C13911yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C13911yescharacteristic
590C2×C22⋊C4D4×C13911yescharacteristic
591C2×C42—21no—
592C2×C42C23×C13911yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C13914yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C13911yescharacteristic
622C24C2×D4×C13911yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C13912yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C13914yes—
657C2×D4C22×C4×C13912yes—
658C2×D4C22×C4×C13912yes—
659C2×D4C2×D4×C13912yes—
660C2×D4#41×C13912yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C13912yes—
688C22×C4C22×C4×C13912yes—
689C22×C4C2×D4×C13911yescharacteristic
690C22×C4C2×D4×C13911yescharacteristic
691C22×C4C2×D4×C13911yescharacteristic
692C22×C4C2×D4×C13911yescharacteristic
693C22×C4C2×D4×C13912yes—
694C22×C4C2×D4×C13912yes—
695C22×C4C24×C13911yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C13912yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C13914yes—
724C4⋊C4C22×C4×C13912yes—
725C4⋊C4C2×D4×C13912yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C13914yes—
734C22⋊C4C22⋊C4×C13914yes—
735C42—42no—
736C42C22×C4×C13912yes—
737C42C2×D4×C13912yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C13912yes—
770C23C2×C22⋊C4×C13912yes—
771C23AGL(1,ℤ/8)×C13912yes—
772C23#137×C13912yes—
773C23C22×D4×C13911yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C13914yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C13912yes—
829C2×C4C2×C22⋊C4×C13912yes—
830C2×C4C2×C22⋊C4×C13912yes—
831C2×C4C2×C22⋊C4×C13912yes—
832C2×C4C23×C4×C13911yescharacteristic
833C2×C4C22×D4×C13911yescharacteristic
834C2×C4C22×D4×C13911yescharacteristic
835C2×C4C2×#41×C13911yescharacteristic
836C2×C4H(5,𝔽2)×C13911yescharacteristic
837C2×C4H(5,𝔽2)×C13911yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C13914yescomplemented
871C22C22×C22⋊C4×C13911yescharacteristic
872C22D42×C13911yescharacteristic
873C22#546×C13911yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
875C22C2×#137×C13911yescharacteristic
876C22#576×C13911yescharacteristic
877C22#577×C13911yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C13911yescharacteristic
889C4#518×C13911yescharacteristic
890C4D42×C13911yescharacteristic
891C4#546×C13911yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C13911yescharacteristic
897C2C2×#417×C13911yescharacteristic
898C2#2897×C13911yescharacteristic
899C2#3264×C13911yescharacteristic
900C2#3266×C13911yescharacteristic
901C2#3306×C13911yescharacteristic
902C2#3314×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#546×C139C2
LCSG ▷ C2×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×#435×C139C2semidirect
3. C2×#417×C139C2semidirect
4. C22×#102×C139C2semidirect
5. D4×C4⋊C4×C139C2semidirect
6. #1983×C139C2semidirect
7. #1959×C139C2semidirect
8. #1895×C139C2semidirect
9. #1892×C139C2semidirect
10. #1874×C139C2semidirect
11. #1872×C139C2semidirect
12. #1802×C139C2semidirect
13. #1788×C139C2semidirect
14. #1786×C139C2semidirect
15. #1762×C139C2semidirect
18. C22×M16×C139C22semidirect
21. #546×C139C4semidirect
32. C22×C4⋊C4×C139C22semidirect
35. C2×C4⋊C8×C139C22semidirect
37. C2×#103×C139C22semidirect
38. C2×#103×C139C22semidirect
39. C2×#103×C139C22semidirect
40. C2×#103×C139C22semidirect
51. C2×C22⋊C8×C139C22semidirect
52. C2×#97×C139C22semidirect
56. #384×C139C22semidirect
58. #380×C139C22semidirect
59. C4×C4⋊C4×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
70. C2×#41×C139C2×C4semidirect
80. C22×D4×C139C2×C4semidirect
101. #124×C139C2×C4semidirect
104. C22⋊Q8×C139C2×C4semidirect
107. #121×C139C2×C4semidirect
112. C4×D4×C139C2×C4semidirect
153. #102×C139D4semidirect
337. D4×C139C4×D4semidirect
418. C22×C139#417semidirect
451. #22419C139direct (N × H)
452. C139#22419direct (N × H)
454. C2×#435C2×C139semidirect
455. C2×#417C2×C139semidirect
456. C22×#102C2×C139semidirect
457. D4×C4⋊C4C2×C139semidirect
458. #1983C2×C139semidirect
459. #1959C2×C139semidirect
460. #1895C2×C139semidirect
461. #1892C2×C139semidirect
462. #1874C2×C139semidirect
463. #1872C2×C139semidirect
464. #1802C2×C139semidirect
465. #1788C2×C139semidirect
466. #1786C2×C139semidirect
467. #1762C2×C139semidirect
470. C22×M16C22×C139semidirect
473. #546C4×C139semidirect
484. C22×C4⋊C4C22×C139semidirect
487. C2×C4⋊C8C22×C139semidirect
489. C2×#103C22×C139semidirect
490. C2×#103C22×C139semidirect
491. C2×#103C22×C139semidirect
492. C2×#103C22×C139semidirect
503. C2×C22⋊C8C22×C139semidirect
504. C2×#97C22×C139semidirect
508. #384C22×C139semidirect
510. #380C22×C139semidirect
511. C4×C4⋊C4C22×C139semidirect
512. #340C22×C139semidirect
513. #340C22×C139semidirect
514. #340C22×C139semidirect
515. #340C22×C139semidirect
522. C2×#41C2×C4×C139semidirect
532. C22×D4C2×C4×C139semidirect
553. #124C2×C4×C139semidirect
556. C22⋊Q8C2×C4×C139semidirect
559. #121C2×C4×C139semidirect
564. C4×D4C2×C4×C139semidirect
605. #102D4×C139semidirect
789. D4C4×D4×C139semidirect
870. C22#417×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×#435×C1392
C2×#417×C1392
C22×#102×C1392
D4×C4⋊C4×C1392
#1983×C1392
#1959×C1392
#1895×C1392
#1892×C1392
#1874×C1392
#1872×C1392
#1802×C1392
#1788×C1392
#1786×C1392
#1762×C1392
#22419139