Finite Group Databasebeta

← C139×#23972 #48018568

Subgroups — C139×#23972 #48018568

Order 35584.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C139C211yesmaximal, characteristic, complemented
2C2×#449×C139C211yesmaximal, characteristic, complemented
3C2×#417×C139C211yesmaximal, characteristic, complemented
4#2407×C139C211yesmaximal, characteristic, complemented
5#2024×C139C211yesmaximal, characteristic, complemented
6#2023×C139C211yesmaximal, characteristic, complemented
7#2000×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1879×C139C211yesmaximal, characteristic, complemented
11#1877×C139C211yesmaximal, characteristic, complemented
12#1874×C139C211yesmaximal, characteristic, complemented
13#1872×C139C211yesmaximal, characteristic, complemented
14#1870×C139C211yesmaximal, characteristic, complemented
15#1824×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139—21no—
17C22×#41×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic
21#547×C139—24no—
22#547×C139—24no—
23C2×C4⋊Q8×C139C2211yescharacteristic
24C2×#123×C139—21no—
25C2×#123×C139—21no—
26C2×C22⋊Q8×C139—21no—
27C2×C22⋊Q8×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C22×C4⋊C4×C139C2211yescharacteristic
34C22×C4⋊C4×C139C2211yescharacteristic
35#449×C139—24no—
36#417×C139—24no—
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48#394×C139—21no—
49#392×C139—21no—
50#391×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#386×C139—21no—
53#385×C139—21no—
54#380×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C2×#41×C139—28no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C2×#41×C139—44no—
71C2×#41×C139—44no—
72C22×Q8×C139—21no—
73C22×Q8×C139C2311yescharacteristic
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139D411yescharacteristic
79C22×D4×C139C2311yescharacteristic
80C22×D4×C139C2311yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139—21no—
83C23×C4×C139—21no—
84C23×C4×C139—21no—
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C2×SD16×C139—22no—
88C2×SD16×C139—22no—
89C2×SD16×C139—41no—
90C2×D8×C139—22no—
91C2×D8×C139—22no—
92C2×D8×C139—41no—
93C2×M16×C139—22no—
94C2×M16×C139—41no—
95C2×M16×C139—41no—
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99C22×C8×C139C2311yescharacteristic
100C4⋊Q8×C139—22no—
101C4⋊Q8×C139—22no—
102#123×C139—28no—
103#123×C139—28no—
104C22⋊Q8×C139—28no—
105C22⋊Q8×C139—22no—
106C22⋊Q8×C139—41no—
107#121×C139—22no—
108#121×C139—22no—
109#121×C139—22no—
110#121×C139—22no—
111#121×C139—41no—
112#121×C139D414yescomplemented
113C4×D4×C139—22no—
114C4×D4×C139—22no—
115C4×D4×C139—22no—
116C4×D4×C139—22no—
117C2×C4⋊C4×C139—21no—
118C2×C4⋊C4×C139—21no—
119C2×C4⋊C4×C139—22no—
120C2×C4⋊C4×C139—21no—
121C2×C4⋊C4×C139—22no—
122C2×C4⋊C4×C139—22no—
123C2×C4⋊C4×C139—21no—
124C2×C4⋊C4×C139D411yescharacteristic
125C2×C4⋊C4×C139D414yescomplemented
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
140C2×C22⋊C4×C139D411yescharacteristic
141C2×C42×C139C2311yescharacteristic
142#103×C139—22no—
143#103×C139—22no—
144#103×C139—22no—
145#102×C139—22no—
146#102×C139—22no—
147#102×C139—22no—
148#102×C139—41no—
149#102×C139—41no—
150C22⋊C8×C139—22no—
151C22⋊C8×C139—41no—
152C22⋊C8×C139—41no—
153#95×C139—21no—
154#95×C139—21no—
155#95×C139—21no—
156C24×C139—21no—
157C24×C139—21no—
158C24×C139C2×D411yescharacteristic
159C24×C139C2×D411yescharacteristic
160#41×C139—28no—
161#41×C139—44no—
162#41×C139—44no—
163#41×C139—44no—
164#41×C139—432no—
165C2×Q8×C139—24no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139—21no—
169C2×Q8×C139—21no—
170C2×Q8×C139—21no—
171C2×Q8×C139—42no—
172C2×Q8×C139—42no—
173C2×Q8×C139#4112yescomplemented
174C2×D4×C139—22no—
175C2×D4×C139—22no—
176C2×D4×C139—24no—
177C2×D4×C139—24no—
178C2×D4×C139—22no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—42no—
197C2×D4×C139—42no—
198C2×D4×C139—81no—
199C2×D4×C139C2×D412yes—
200C2×D4×C139#4112yescomplemented
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—24no—
206C22×C4×C139—24no—
207C22×C4×C139—24no—
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—21no—
220C22×C4×C139—42no—
221C22×C4×C139—42no—
222C22×C4×C139—42no—
223C22×C4×C139—42no—
224C22×C4×C139—42no—
225C22×C4×C139—42no—
226C22×C4×C139—42no—
227C22×C4×C139—42no—
228C22×C4×C139—42no—
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D412yes—
233C22×C4×C139C2×D412yes—
234C22×C4×C139C2×D411yescharacteristic
235C22×C4×C139C2411yescharacteristic
236SD16×C139—44no—
237D8×C139—44no—
238M16×C139—44no—
239C2×C8×C139—21no—
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—
251C4⋊C4×C139—24no—
252C4⋊C4×C139—24no—
253C4⋊C4×C139—24no—
254C4⋊C4×C139—22no—
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—42no—
263C4⋊C4×C139C2×D412yes—
264C4⋊C4×C139C2×D412yes—
265C4⋊C4×C139C2×D412yes—
266C22⋊C4×C139—24no—
267C22⋊C4×C139—24no—
268C22⋊C4×C139—22no—
269C22⋊C4×C139—24no—
270C22⋊C4×C139—22no—
271C22⋊C4×C139—42no—
272C22⋊C4×C139—42no—
273C22⋊C4×C139—42no—
274C22⋊C4×C139—81no—
275C22⋊C4×C139—81no—
276C42×C139—21no—
277C42×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—21no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—22no—
291C23×C139—22no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
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#12012yes—
305C23×C139AGL(1,ℤ/8)12yes—
306C23×C139C22×D411yescharacteristic
307Q8×C139—22no—
308Q8×C139—22no—
309Q8×C139—48no—
310Q8×C139—41no—
311Q8×C139—41no—
312D4×C139—28no—
313D4×C139—22no—
314D4×C139—22no—
315D4×C139—22no—
316D4×C139—22no—
317D4×C139—48no—
318D4×C139—48no—
319D4×C139—48no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—84no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—22no—
330C2×C4×C139—22no—
331C2×C4×C139—22no—
332C2×C4×C139—22no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—22no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—21no—
339C2×C4×C139—22no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—48no—
344C2×C4×C139—48no—
345C2×C4×C139—48no—
346C2×C4×C139—48no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
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#12012yes—
366C2×C4×C139AGL(1,ℤ/8)12yes—
367C2×C4×C139C22×D411yescharacteristic
368C2×C4×C139C22×D411yescharacteristic
369C2×C4×C139C2×#4111yescharacteristic
370C2×C4×C139C2×#4111yescharacteristic
371C2×C4×C139H(5,𝔽2)11yescharacteristic
372C2×C4×C139H(5,𝔽2)11yescharacteristic
373C8×C139—41no—
374C8×C139—41no—
375C8×C139—41no—
376C8×C139—41no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—22no—
381C22×C139—22no—
382C22×C139—22no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—41no—
387C22×C139—41no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—41no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—42no—
394C22×C139—42no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—81no—
398C22×C139—81no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139C2×#12011yescharacteristic
406C22×C139#54611yescharacteristic
407C22×C139#54611yescharacteristic
408C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C139#57711yescharacteristic
411C22×C139#57811yescharacteristic
412C4×C139—22no—
413C4×C139—22no—
414C4×C139—41no—
415C4×C139—42no—
416C4×C139—42no—
417C4×C139—42no—
418C4×C139—42no—
419C4×C139—41no—
420C4×C139—81no—
421C4×C139—81no—
422C4×C139#52511yescharacteristic
423C4×C139#53511yescharacteristic
424C4×C139#54611yescharacteristic
425C4×C139#54611yescharacteristic
426C2×C139—42no—
427C2×C139—42no—
428C2×C139—82no—
429C2×C139—82no—
430C2×C139#240411yescharacteristic
431C2×C139#300311yescharacteristic
432C2×C139#301311yescharacteristic
433C2×C139#330611yescharacteristic
434C2×C139#330811yescharacteristic
435C2×C139#333011yescharacteristic
436C2×C139#333211yescharacteristic
437#23972C13911yesmaximal, characteristic, direct product factor, Sylow
438C139#2397211yescharacteristic, direct product factor, Sylow
439C2×#547C2×C13911yescharacteristic, complemented
440C2×#449C2×C13911yescharacteristic, complemented
441C2×#417C2×C13911yescharacteristic, complemented
442#2407C2×C13911yescharacteristic, complemented
443#2024C2×C13911yescharacteristic, complemented
444#2023C2×C13911yescharacteristic, complemented
445#2000C2×C13911yescharacteristic, complemented
446#1999C2×C13911yescharacteristic, complemented
447#1895C2×C13911yescharacteristic, complemented
448#1879C2×C13911yescharacteristic, complemented
449#1877C2×C13911yescharacteristic, complemented
450#1874C2×C13911yescharacteristic, complemented
451#1872C2×C13911yescharacteristic, complemented
452#1870C2×C13911yescharacteristic, complemented
453#1824C2×C13911yescharacteristic, complemented
454C22×#41—21no—
455C22×#41C22×C13911yescharacteristic
456C22×SD16C22×C13911yescharacteristic
457C22×D8C22×C13911yescharacteristic
458C22×M16C22×C13911yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C13911yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C13911yescharacteristic
466C2×#121C22×C13911yescharacteristic
467C2×#121C22×C13911yescharacteristic
468C2×#121C22×C13911yescharacteristic
469C2×C4×D4C22×C13911yescharacteristic
470C2×C4×D4C22×C13911yescharacteristic
471C22×C4⋊C4C22×C13911yescharacteristic
472C22×C4⋊C4C22×C13911yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C13911yescharacteristic
476C2×#103C22×C13911yescharacteristic
477C2×#103C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×#102C22×C13911yescharacteristic
480C2×#102C22×C13911yescharacteristic
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×C22⋊C8C22×C13911yescharacteristic
484C2×C22⋊C8C22×C13911yescharacteristic
485C2×C22⋊C8C22×C13911yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C13911yescharacteristic
489#390C22×C13911yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C13911yescharacteristic
493#340C22×C13911yescharacteristic
494#340C22×C13911yescharacteristic
495#340C22×C13911yescharacteristic
496#340C22×C13911yescharacteristic
497#340C22×C13911yescharacteristic
498#340C22×C13911yescharacteristic
499#336C22×C13911yescharacteristic
500#336C22×C13911yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C13911yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C13911yescharacteristic
517C22×D4C23×C13911yescharacteristic
518C22×D4C23×C13911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C13911yescharacteristic
524C23×C4C23×C13911yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C13911yescharacteristic
535C22×C8C23×C13911yescharacteristic
536C22×C8C23×C13911yescharacteristic
537C22×C8C23×C13911yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C13914yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C13911yescharacteristic
563C2×C4⋊C4D4×C13914yescomplemented
564C2×C4⋊C4C23×C13911yescharacteristic
565C2×C4⋊C4C23×C13911yescharacteristic
566C2×C4⋊C4C23×C13911yescharacteristic
567C2×C4⋊C4C23×C13911yescharacteristic
568C2×C4⋊C4C23×C13911yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C13911yescharacteristic
578C2×C22⋊C4D4×C13911yescharacteristic
579C2×C42C23×C13911yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C13911yescharacteristic
597C24C2×D4×C13911yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C13912yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C13912yes—
638C2×D4#41×C13912yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C13911yescharacteristic
668C22×C4C2×D4×C13911yescharacteristic
669C22×C4C2×D4×C13911yescharacteristic
670C22×C4C2×D4×C13912yes—
671C22×C4C2×D4×C13912yes—
672C22×C4C2×D4×C13911yescharacteristic
673C22×C4C24×C13911yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C13912yes—
702C4⋊C4C2×D4×C13912yes—
703C4⋊C4C2×D4×C13912yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C13912yes—
743C23AGL(1,ℤ/8)×C13912yes—
744C23C22×D4×C13911yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C13912yes—
804C2×C4AGL(1,ℤ/8)×C13912yes—
805C2×C4C22×D4×C13911yescharacteristic
806C2×C4C22×D4×C13911yescharacteristic
807C2×C4C2×#41×C13911yescharacteristic
808C2×C4C2×#41×C13911yescharacteristic
809C2×C4H(5,𝔽2)×C13911yescharacteristic
810C2×C4H(5,𝔽2)×C13911yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C13911yescharacteristic
844C22#546×C13911yescharacteristic
845C22#546×C13911yescharacteristic
846C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
847C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
848C22#577×C13911yescharacteristic
849C22#578×C13911yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C13911yescharacteristic
861C4#535×C13911yescharacteristic
862C4#546×C13911yescharacteristic
863C4#546×C13911yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2#2404×C13911yescharacteristic
869C2#3003×C13911yescharacteristic
870C2#3013×C13911yescharacteristic
871C2#3306×C13911yescharacteristic
872C2#3308×C13911yescharacteristic
873C2#3330×C13911yescharacteristic
874C2#3332×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C139C2semidirect
2. C2×#449×C139C2semidirect
3. C2×#417×C139C2semidirect
4. #2407×C139C2semidirect
5. #2024×C139C2semidirect
6. #2023×C139C2semidirect
7. #2000×C139C2semidirect
8. #1999×C139C2semidirect
9. #1895×C139C2semidirect
10. #1879×C139C2semidirect
11. #1877×C139C2semidirect
12. #1874×C139C2semidirect
13. #1872×C139C2semidirect
14. #1870×C139C2semidirect
15. #1824×C139C2semidirect
112. #121×C139D4semidirect
125. C2×C4⋊C4×C139D4semidirect
173. C2×Q8×C139#41semidirect
200. C2×D4×C139#41semidirect
437. #23972C139direct (N × H)
438. C139#23972direct (N × H)
439. C2×#547C2×C139semidirect
440. C2×#449C2×C139semidirect
441. C2×#417C2×C139semidirect
442. #2407C2×C139semidirect
443. #2024C2×C139semidirect
444. #2023C2×C139semidirect
445. #2000C2×C139semidirect
446. #1999C2×C139semidirect
447. #1895C2×C139semidirect
448. #1879C2×C139semidirect
449. #1877C2×C139semidirect
450. #1874C2×C139semidirect
451. #1872C2×C139semidirect
452. #1870C2×C139semidirect
453. #1824C2×C139semidirect
550. #121D4×C139semidirect
563. C2×C4⋊C4D4×C139semidirect
611. C2×Q8#41×C139semidirect
638. C2×D4#41×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1392
C2×#449×C1392
C2×#417×C1392
#2407×C1392
#2024×C1392
#2023×C1392
#2000×C1392
#1999×C1392
#1895×C1392
#1879×C1392
#1877×C1392
#1874×C1392
#1872×C1392
#1870×C1392
#1824×C1392
#23972139