Finite Group Databasebeta

← C139×#22414 #48017010

Subgroups — C139×#22414 #48017010

Order 35584.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C139C211yesmaximal, characteristic
2C2×C8×D4×C139C211yesmaximal, characteristic, complemented
3C2×#416×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2352×C139C211yesmaximal, characteristic, complemented
6#1983×C139C211yesmaximal, characteristic, complemented
7#1958×C139C211yesmaximal, characteristic, complemented
8#1893×C139C211yesmaximal, characteristic, complemented
9#1892×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1872×C139C211yesmaximal, characteristic, complemented
12#1804×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic, complemented
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×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic, complemented
31C22×C4⋊C4×C139C2211yescharacteristic
32C22×C22⋊C4×C139—21no—
33C8×D4×C139—24no—
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35#416×C139—24no—
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#103×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#102×C139—24no—
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50C2×C22⋊C8×C139C2211yescharacteristic, complemented
51C2×C4×C8×C139C2211yescharacteristic, complemented
52#388×C139—21no—
53#387×C139—21no—
54#386×C139—21no—
55#382×C139C2211yescharacteristic, complemented
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic, complemented
58C4×C4⋊C4×C139C2211yescharacteristic, complemented
59C4×C22⋊C4×C139—21no—
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×C414yes—
81C22×D4×C139D411yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2311yescharacteristic
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139—21no—
87C23×C4×C139C2311yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C22×C8×C139—22no—
90C22×C8×C139—22no—
91C22×C8×C139—22no—
92C22×C8×C139—22no—
93C22×C8×C139—41no—
94C22×C8×C139—41no—
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99#124×C139—22no—
100#124×C139C2×C414yescomplemented
101#123×C139—28no—
102C22⋊Q8×C139—22no—
103C22⋊Q8×C139C2×C414yes—
104#121×C139—22no—
105#121×C139—28no—
106#121×C139C2×C414yescomplemented
107#120×C139—28no—
108C4×D4×C139—22no—
109C4×D4×C139C2×C414yes—
110C4×D4×C139C2×C414yescomplemented
111C4×D4×C139D414yes—
112#117×C139—22no—
113#117×C139—41no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—22no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139—41no—
118C2×C4⋊C4×C139D411yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C4⋊C4×C139C2311yescharacteristic
122C2×C4⋊C4×C139C2311yescharacteristic
123C2×C4⋊C4×C139C2311yescharacteristic
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—28no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139D411yescharacteristic
134C2×C22⋊C4×C139D411yescharacteristic
135C2×C42×C139—21no—
136C2×C42×C139—21no—
137C2×C42×C139C2311yescharacteristic
138C4⋊C8×C139—22no—
139#103×C139—22no—
140#103×C139—22no—
141#103×C139—41no—
142#103×C139—41no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139—22no—
146#102×C139—22no—
147#102×C139—22no—
148#102×C139—41no—
149#102×C139—41no—
150#102×C139D414yescomplemented
151C22⋊C8×C139—22no—
152C22⋊C8×C139—22no—
153C4×C8×C139—22no—
154#95×C139—21no—
155#95×C139—21no—
156#95×C139—21no—
157#95×C139—21no—
158#95×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—24no—
162C24×C139—42no—
163C24×C139—42no—
164C24×C139—42no—
165C24×C139—42no—
166C24×C139—81no—
167C24×C139—81no—
168C24×C139C2×D411yescharacteristic
169C24×C139C2×D411yescharacteristic
170#41×C139—28no—
171#41×C139—44no—
172#41×C139—44no—
173#41×C139—44no—
174C2×Q8×C139—21no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139C22×C412yes—
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—28no—
183C2×D4×C139—24no—
184C2×D4×C139—24no—
185C2×D4×C139—24no—
186C2×D4×C139—21no—
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—44no—
195C2×D4×C139—44no—
196C2×D4×C139—44no—
197C2×D4×C139—42no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—81no—
202C2×D4×C139—81no—
203C2×D4×C139C22⋊C414yes—
204C2×D4×C139C22×C412yes—
205C2×D4×C139C22×C412yes—
206C2×D4×C139C2×D412yes—
207C2×D4×C139#4112yes—
208C22×C4×C139—21no—
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—24no—
220C22×C4×C139—24no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—42no—
225C22×C4×C139—42no—
226C22×C4×C139—42no—
227C22×C4×C139—42no—
228C22×C4×C139—81no—
229C22×C4×C139—81no—
230C22×C4×C139—81no—
231C22×C4×C139C22×C412yes—
232C22×C4×C139C22×C412yes—
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D411yescharacteristic
235C22×C4×C139C2×D411yescharacteristic
236C22×C4×C139C2×D411yescharacteristic
237C22×C4×C139C2×D412yes—
238C22×C4×C139C2×D412yes—
239C22×C4×C139C2411yescharacteristic
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—21no—
244C2×C8×C139—21no—
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—44no—
252C2×C8×C139—44no—
253C2×C8×C139C2×D412yes—
254C4⋊C4×C139—24no—
255C4⋊C4×C139—21no—
256C4⋊C4×C139—21no—
257C4⋊C4×C139—21no—
258C4⋊C4×C139—21no—
259C4⋊C4×C139—21no—
260C4⋊C4×C139—21no—
261C4⋊C4×C139—21no—
262C4⋊C4×C139—21no—
263C4⋊C4×C139—42no—
264C4⋊C4×C139C22⋊C414yes—
265C4⋊C4×C139C22×C412yes—
266C4⋊C4×C139C2×D412yes—
267C22⋊C4×C139—24no—
268C22⋊C4×C139—24no—
269C22⋊C4×C139—24no—
270C22⋊C4×C139—24no—
271C22⋊C4×C139—24no—
272C22⋊C4×C139—42no—
273C22⋊C4×C139—42no—
274C22⋊C4×C139—81no—
275C22⋊C4×C139C22⋊C414yes—
276C22⋊C4×C139C22⋊C414yes—
277C42×C139—42no—
278C42×C139—81no—
279C42×C139C22×C412yes—
280C42×C139C2×D412yes—
281C23×C139—21no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—22no—
286C23×C139—21no—
287C23×C139—22no—
288C23×C139—21no—
289C23×C139—22no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—22no—
295C23×C139—48no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—48no—
307C23×C139—84no—
308C23×C139—84no—
309C23×C139—84no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139C2×C22⋊C412yes—
313C23×C139C2×C22⋊C412yes—
314C23×C139#13512yes—
315C23×C139#13512yes—
316C23×C139C22×D411yescharacteristic
317Q8×C139—22no—
318Q8×C139—22no—
319Q8×C139—41no—
320Q8×C139—41no—
321D4×C139—28no—
322D4×C139—22no—
323D4×C139—22no—
324D4×C139—22no—
325D4×C139—22no—
326D4×C139—22no—
327D4×C139—48no—
328D4×C139—48no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—84no—
332D4×C139C4×D414yes—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—22no—
342C2×C4×C139—22no—
343C2×C4×C139—22no—
344C2×C4×C139—22no—
345C2×C4×C139—22no—
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—48no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
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—84no—
369C2×C4×C139—84no—
370C2×C4×C139C2×C22⋊C412yes—
371C2×C4×C139C2×C22⋊C412yes—
372C2×C4×C139C2×C22⋊C412yes—
373C2×C4×C139C2×C22⋊C412yes—
374C2×C4×C139C23×C411yescharacteristic
375C2×C4×C139C22×D411yescharacteristic
376C2×C4×C139C22×D411yescharacteristic
377C2×C4×C139C2×#4111yescharacteristic
378C2×C4×C139H(5,𝔽2)11yescharacteristic
379C2×C4×C139H(5,𝔽2)11yescharacteristic
380C8×C139—22no—
381C8×C139—41no—
382C8×C139—41no—
383C8×C139—41no—
384C22×C139—22no—
385C22×C139—22no—
386C22×C139—22no—
387C22×C139—22no—
388C22×C139—22no—
389C22×C139—22no—
390C22×C139—22no—
391C22×C139—24no—
392C22×C139—22no—
393C22×C139—22no—
394C22×C139—42no—
395C22×C139—42no—
396C22×C139—41no—
397C22×C139—42no—
398C22×C139—41no—
399C22×C139—42no—
400C22×C139—41no—
401C22×C139—42no—
402C22×C139—41no—
403C22×C139—42no—
404C22×C139—42no—
405C22×C139—42no—
406C22×C139—42no—
407C22×C139—816no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139#41614yescomplemented
413C22×C139C22×C22⋊C411yescharacteristic
414C22×C139D4211yescharacteristic
415C22×C139#54611yescharacteristic
416C22×C139C2×#13511yescharacteristic
417C22×C139C2×#13511yescharacteristic
418C22×C139#57611yescharacteristic
419C22×C139#57711yescharacteristic
420C4×C139—22no—
421C4×C139—22no—
422C4×C139—22no—
423C4×C139—22no—
424C4×C139—42no—
425C4×C139—42no—
426C4×C139—42no—
427C4×C139—81no—
428C4×C139—81no—
429C4×C139—81no—
430C4×C139C2×C4×D411yescharacteristic
431C4×C139#51811yescharacteristic
432C4×C139D4211yescharacteristic
433C4×C139#54611yescharacteristic
434C2×C139—24no—
435C2×C139—42no—
436C2×C139—44no—
437C2×C139—82no—
438C2×C139D4×C22⋊C411yescharacteristic
439C2×C139C2×#41611yescharacteristic
440C2×C139#289711yescharacteristic
441C2×C139#328011yescharacteristic
442C2×C139#328211yescharacteristic
443C2×C139#329611yescharacteristic
444C2×C139#329711yescharacteristic
445#22414C13911yesmaximal, characteristic, direct product factor, Sylow
446C139#2241411yescharacteristic, direct product factor, Sylow
447C2×#546C2×C13911yescharacteristic
448C2×C8×D4C2×C13911yescharacteristic, complemented
449C2×#416C2×C13911yescharacteristic, complemented
450C22×#102C2×C13911yescharacteristic, complemented
451#2352C2×C13911yescharacteristic, complemented
452#1983C2×C13911yescharacteristic, complemented
453#1958C2×C13911yescharacteristic, complemented
454#1893C2×C13911yescharacteristic, complemented
455#1892C2×C13911yescharacteristic, complemented
456#1875C2×C13911yescharacteristic, complemented
457#1872C2×C13911yescharacteristic, complemented
458#1804C2×C13911yescharacteristic, complemented
459#1788C2×C13911yescharacteristic, complemented
460#1786C2×C13911yescharacteristic, complemented
461C4×#102C2×C13911yescharacteristic, complemented
462C22×#41C22×C13911yescharacteristic
463C23×D4C22×C13911yescharacteristic
464C23×C8C22×C13911yescharacteristic
465C23×C8C22×C13911yescharacteristic, complemented
466#546—24no—
467#546C4×C13918yescomplemented
468C2×#124C22×C13911yescharacteristic
469C2×#123—21no—
470C2×C22⋊Q8C22×C13911yescharacteristic
471C2×#121—21no—
472C2×#121C22×C13911yescharacteristic
473C2×#120—21no—
474C2×C4×D4C22×C13911yescharacteristic
475C2×C4×D4C22×C13911yescharacteristic
476C2×#117C22×C13911yescharacteristic, complemented
477C22×C4⋊C4C22×C13911yescharacteristic
478C22×C22⋊C4—21no—
479C8×D4—24no—
480C2×C4⋊C8C22×C13911yescharacteristic, complemented
481#416—24no—
482C2×#103C22×C13911yescharacteristic, complemented
483C2×#103C22×C13911yescharacteristic, complemented
484C2×#103C22×C13911yescharacteristic, complemented
485C2×#103C22×C13911yescharacteristic, complemented
486C2×#102—24no—
487C2×#102C22×C13911yescharacteristic
488C2×#102C22×C13911yescharacteristic
489C2×#102C22×C13911yescharacteristic
490C2×#102C22×C13911yescharacteristic
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic
493C2×#102C22×C13911yescharacteristic
494C2×#102C22×C13911yescharacteristic
495C2×C22⋊C8C22×C13911yescharacteristic
496C2×C22⋊C8C22×C13911yescharacteristic, complemented
497C2×C4×C8C22×C13911yescharacteristic, complemented
498#388—21no—
499#387—21no—
500#386—21no—
501#382C22×C13911yescharacteristic, complemented
502#380C22×C13911yescharacteristic
503#380C22×C13911yescharacteristic, complemented
504C4×C4⋊C4C22×C13911yescharacteristic, complemented
505C4×C22⋊C4—21no—
506#340C22×C13911yescharacteristic, complemented
507#340C22×C13911yescharacteristic, complemented
508#340C22×C13911yescharacteristic, complemented
509#340C22×C13911yescharacteristic, complemented
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C13914yescomplemented
517C22×Q8C23×C13911yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C13914yes—
527C22×D4D4×C13911yescharacteristic
528C22×D4C23×C13911yescharacteristic
529C22×D4C23×C13911yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C13911yescharacteristic
534C23×C4C23×C13911yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C23×C13911yescharacteristic
542C22×C8C23×C13911yescharacteristic
543C22×C8C23×C13911yescharacteristic
544C22×C8C23×C13911yescharacteristic
545#124—22no—
546#124C2×C4×C13914yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C13914yes—
550#121—22no—
551#121—28no—
552#121C2×C4×C13914yescomplemented
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C13914yes—
556C4×D4C2×C4×C13914yescomplemented
557C4×D4D4×C13914yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C13911yescharacteristic
565C2×C4⋊C4C23×C13911yescharacteristic
566C2×C4⋊C4C23×C13911yescharacteristic
567C2×C4⋊C4C23×C13911yescharacteristic
568C2×C4⋊C4C23×C13911yescharacteristic
569C2×C4⋊C4C23×C13911yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C13911yescharacteristic
580C2×C22⋊C4D4×C13911yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C13911yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C13914yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C13911yescharacteristic
615C24C2×D4×C13911yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C13912yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—28no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C13914yes—
650C2×D4C22×C4×C13912yes—
651C2×D4C22×C4×C13912yes—
652C2×D4C2×D4×C13912yes—
653C2×D4#41×C13912yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C13912yes—
678C22×C4C22×C4×C13912yes—
679C22×C4C2×D4×C13911yescharacteristic
680C22×C4C2×D4×C13911yescharacteristic
681C22×C4C2×D4×C13911yescharacteristic
682C22×C4C2×D4×C13911yescharacteristic
683C22×C4C2×D4×C13912yes—
684C22×C4C2×D4×C13912yes—
685C22×C4C24×C13911yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—44no—
698C2×C8—44no—
699C2×C8C2×D4×C13912yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C13914yes—
711C4⋊C4C22×C4×C13912yes—
712C4⋊C4C2×D4×C13912yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C13914yes—
722C22⋊C4C22⋊C4×C13914yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C13912yes—
726C42C2×D4×C13912yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C2×C22⋊C4×C13912yes—
759C23C2×C22⋊C4×C13912yes—
760C23#135×C13912yes—
761C23#135×C13912yes—
762C23C22×D4×C13911yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C13914yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C13912yes—
817C2×C4C2×C22⋊C4×C13912yes—
818C2×C4C2×C22⋊C4×C13912yes—
819C2×C4C2×C22⋊C4×C13912yes—
820C2×C4C23×C4×C13911yescharacteristic
821C2×C4C22×D4×C13911yescharacteristic
822C2×C4C22×D4×C13911yescharacteristic
823C2×C4C2×#41×C13911yescharacteristic
824C2×C4H(5,𝔽2)×C13911yescharacteristic
825C2×C4H(5,𝔽2)×C13911yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—816no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#416×C13914yescomplemented
859C22C22×C22⋊C4×C13911yescharacteristic
860C22D42×C13911yescharacteristic
861C22#546×C13911yescharacteristic
862C22C2×#135×C13911yescharacteristic
863C22C2×#135×C13911yescharacteristic
864C22#576×C13911yescharacteristic
865C22#577×C13911yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C13911yescharacteristic
877C4#518×C13911yescharacteristic
878C4D42×C13911yescharacteristic
879C4#546×C13911yescharacteristic
880C2—24no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C13911yescharacteristic
885C2C2×#416×C13911yescharacteristic
886C2#2897×C13911yescharacteristic
887C2#3280×C13911yescharacteristic
888C2#3282×C13911yescharacteristic
889C2#3296×C13911yescharacteristic
890C2#3297×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×C8×D4×C139C2semidirect
3. C2×#416×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2352×C139C2semidirect
6. #1983×C139C2semidirect
7. #1958×C139C2semidirect
8. #1893×C139C2semidirect
9. #1892×C139C2semidirect
10. #1875×C139C2semidirect
11. #1872×C139C2semidirect
12. #1804×C139C2semidirect
13. #1788×C139C2semidirect
14. #1786×C139C2semidirect
15. C4×#102×C139C2semidirect
19. C23×C8×C139C22semidirect
21. #546×C139C4semidirect
30. C2×#117×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
36. C2×#103×C139C22semidirect
37. C2×#103×C139C22semidirect
38. C2×#103×C139C22semidirect
39. C2×#103×C139C22semidirect
50. C2×C22⋊C8×C139C22semidirect
51. C2×C4×C8×C139C22semidirect
55. #382×C139C22semidirect
57. #380×C139C22semidirect
58. C4×C4⋊C4×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
70. C2×#41×C139C2×C4semidirect
100. #124×C139C2×C4semidirect
106. #121×C139C2×C4semidirect
110. C4×D4×C139C2×C4semidirect
150. #102×C139D4semidirect
412. C22×C139#416semidirect
445. #22414C139direct (N × H)
446. C139#22414direct (N × H)
448. C2×C8×D4C2×C139semidirect
449. C2×#416C2×C139semidirect
450. C22×#102C2×C139semidirect
451. #2352C2×C139semidirect
452. #1983C2×C139semidirect
453. #1958C2×C139semidirect
454. #1893C2×C139semidirect
455. #1892C2×C139semidirect
456. #1875C2×C139semidirect
457. #1872C2×C139semidirect
458. #1804C2×C139semidirect
459. #1788C2×C139semidirect
460. #1786C2×C139semidirect
461. C4×#102C2×C139semidirect
465. C23×C8C22×C139semidirect
467. #546C4×C139semidirect
476. C2×#117C22×C139semidirect
480. C2×C4⋊C8C22×C139semidirect
482. C2×#103C22×C139semidirect
483. C2×#103C22×C139semidirect
484. C2×#103C22×C139semidirect
485. C2×#103C22×C139semidirect
496. C2×C22⋊C8C22×C139semidirect
497. C2×C4×C8C22×C139semidirect
501. #382C22×C139semidirect
503. #380C22×C139semidirect
504. C4×C4⋊C4C22×C139semidirect
506. #340C22×C139semidirect
507. #340C22×C139semidirect
508. #340C22×C139semidirect
509. #340C22×C139semidirect
516. C2×#41C2×C4×C139semidirect
546. #124C2×C4×C139semidirect
552. #121C2×C4×C139semidirect
556. C4×D4C2×C4×C139semidirect
596. #102D4×C139semidirect
858. C22#416×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×C8×D4×C1392
C2×#416×C1392
C22×#102×C1392
#2352×C1392
#1983×C1392
#1958×C1392
#1893×C1392
#1892×C1392
#1875×C1392
#1872×C1392
#1804×C1392
#1788×C1392
#1786×C1392
C4×#102×C1392
#22414139