Finite Group Databasebeta

← C139×#25124 #48019720

Subgroups — C139×#25124 #48019720

Order 35584.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#447×C139C211yesmaximal, characteristic, complemented
3C2×#435×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2416×C139C211yesmaximal, characteristic, complemented
6#2408×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2034×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1972×C139C211yesmaximal, characteristic, complemented
12#1936×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1893×C139C211yesmaximal, characteristic, complemented
15#1853×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic, complemented
20C23×C8×C139C2211yescharacteristic
21C2×#121×C139—21no—
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic, complemented
26C2×#120×C139—21no—
27C2×C4×D4×C139C2211yescharacteristic
28C22×C4⋊C4×C139C2211yescharacteristic
29#469×C139—24no—
30#447×C139—24no—
31#435×C139—24no—
32C2×#106×C139C2211yescharacteristic, complemented
33C2×#106×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35C2×#102×C139—24no—
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic, complemented
43C2×#102×C139C2211yescharacteristic, complemented
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic, complemented
46C2×#97×C139C2211yescharacteristic, complemented
47#396×C139—21no—
48#394×C139—21no—
49#394×C139—21no—
50#392×C139—21no—
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#390×C139C2211yescharacteristic, complemented
54#389×C139C2211yescharacteristic, complemented
55#386×C139—21no—
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic, complemented
58#379×C139—21no—
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—22no—
71C22×D4×C139—21no—
72C22×D4×C139—22no—
73C22×D4×C139—41no—
74C22×D4×C139—41no—
75C22×D4×C139D411yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78C22×D4×C139C2311yescharacteristic
79C23×C4×C139—21no—
80C23×C4×C139C2311yescharacteristic
81C23×C4×C139C2311yescharacteristic
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—41no—
87C2×D8×C139—41no—
88C2×M16×C139—22no—
89C2×M16×C139—22no—
90C2×M16×C139—41no—
91C22×C8×C139—22no—
92C22×C8×C139—22no—
93C22×C8×C139—41no—
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—41no—
104#121×C139—41no—
105#121×C139—41no—
106#121×C139—44no—
107#120×C139—44no—
108C4×D4×C139—22no—
109C4×D4×C139—22no—
110C2×C4⋊C4×C139—22no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—41no—
114C2×C4⋊C4×C139D411yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
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—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139D411yescharacteristic
133C2×C22⋊C4×C139D411yescharacteristic
134C2×C42×C139C2311yescharacteristic
135#106×C139—22no—
136#106×C139—41no—
137C4⋊C8×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139—41no—
145#102×C139D414yescomplemented
146C22⋊C8×C139—22no—
147C22⋊C8×C139D414yescomplemented
148#97×C139—22no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—81no—
161C24×C139—81no—
162C24×C139C2×D411yescharacteristic
163C24×C139C2×D411yescharacteristic
164C2×D4×C139—28no—
165C2×D4×C139—22no—
166C2×D4×C139—22no—
167C2×D4×C139—22no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—44no—
185C2×D4×C139—44no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—44no—
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—42no—
199C2×D4×C139—81no—
200C2×D4×C139—81no—
201C2×D4×C139—81no—
202C2×D4×C139C2×D412yes—
203C2×D4×C139#4112yes—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
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—42no—
220C22×C4×C139—42no—
221C22×C4×C139—81no—
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139C2×D411yescharacteristic
225C22×C4×C139C2×D411yescharacteristic
226C22×C4×C139C2×D412yes—
227C22×C4×C139#4112yes—
228C22×C4×C139C2411yescharacteristic
229D8×C139—44no—
230D8×C139—44no—
231M16×C139—44no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—44no—
242C2×C8×C139C2×D412yes—
243C2×C8×C139C2×D412yes—
244C2×C8×C139C2×D412yes—
245C4⋊C4×C139—22no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139—21no—
255C4⋊C4×C139—42no—
256C4⋊C4×C139—42no—
257C4⋊C4×C139C2×D412yes—
258C22⋊C4×C139—22no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—42no—
263C22⋊C4×C139—42no—
264C22⋊C4×C139—42no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—42no—
268C22⋊C4×C139—42no—
269C22⋊C4×C139—81no—
270C22⋊C4×C139—81no—
271C22⋊C4×C139—81no—
272C42×C139—21no—
273C42×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—22no—
280C23×C139—21no—
281C23×C139—22no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—48no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
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—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—84no—
308C23×C139—84no—
309C23×C139—84no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139—84no—
313C23×C139#12112yes—
314C23×C139AGL(1,ℤ/8)12yes—
315C23×C139AGL(1,ℤ/8)12yes—
316C23×C139C22×D411yescharacteristic
317D4×C139—22no—
318D4×C139—22no—
319D4×C139—22no—
320D4×C139—22no—
321D4×C139—48no—
322D4×C139—44no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—84no—
332D4×C139—84no—
333D4×C139—84no—
334D4×C139—84no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—22no—
340C2×C4×C139—22no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—22no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
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—41no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—84no—
370C2×C4×C139#12112yes—
371C2×C4×C139C22×D411yescharacteristic
372C2×C4×C139C22×D411yescharacteristic
373C2×C4×C139C2×#4111yescharacteristic
374C2×C4×C139C2×#4111yescharacteristic
375C2×C4×C139H(5,𝔽2)11yescharacteristic
376C2×C4×C139H(5,𝔽2)11yescharacteristic
377C8×C139—22no—
378C8×C139—22no—
379C8×C139—22no—
380C8×C139—41no—
381C22×C139—22no—
382C22×C139—22no—
383C22×C139—22no—
384C22×C139—22no—
385C22×C139—22no—
386C22×C139—22no—
387C22×C139—41no—
388C22×C139—42no—
389C22×C139—42no—
390C22×C139—41no—
391C22×C139—42no—
392C22×C139—41no—
393C22×C139—42no—
394C22×C139—41no—
395C22×C139—42no—
396C22×C139—41no—
397C22×C139—41no—
398C22×C139—41no—
399C22×C139—42no—
400C22×C139—816no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139—81no—
414C22×C139—81no—
415C22×C139—81no—
416C22×C139#46914yescomplemented
417C22×C139C2×#12111yescharacteristic
418C22×C139D4211yescharacteristic
419C22×C139#54611yescharacteristic
420C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C139#57611yescharacteristic
423C22×C139#57711yescharacteristic
424C4×C139—22no—
425C4×C139—41no—
426C4×C139—42no—
427C4×C139—41no—
428C4×C139—41no—
429C4×C139—81no—
430C4×C139—81no—
431C4×C139—81no—
432C4×C139—81no—
433C4×C139#52511yescharacteristic
434C4×C139#53811yescharacteristic
435C4×C139D4211yescharacteristic
436C4×C139#54611yescharacteristic
437C2×C139—24no—
438C2×C139—81no—
439C2×C139—82no—
440C2×C139—82no—
441C2×C139—161no—
442C2×C139#242411yescharacteristic
443C2×C139C2×#46911yescharacteristic
444C2×C139#306211yescharacteristic
445C2×C139#326411yescharacteristic
446C2×C139#326511yescharacteristic
447C2×C139#330611yescharacteristic
448C2×C139#331811yescharacteristic
449#25124C13911yesmaximal, characteristic, direct product factor, Sylow
450C139#2512411yescharacteristic, direct product factor, Sylow
451C2×#469C2×C13911yescharacteristic, complemented
452C2×#447C2×C13911yescharacteristic, complemented
453C2×#435C2×C13911yescharacteristic, complemented
454C22×#102C2×C13911yescharacteristic, complemented
455#2416C2×C13911yescharacteristic, complemented
456#2408C2×C13911yescharacteristic, complemented
457#2065C2×C13911yescharacteristic, complemented
458#2054C2×C13911yescharacteristic, complemented
459#2034C2×C13911yescharacteristic, complemented
460#1999C2×C13911yescharacteristic, complemented
461#1972C2×C13911yescharacteristic, complemented
462#1936C2×C13911yescharacteristic, complemented
463#1895C2×C13911yescharacteristic, complemented
464#1893C2×C13911yescharacteristic, complemented
465#1853C2×C13911yescharacteristic, complemented
466C23×D4C22×C13911yescharacteristic
467C22×D8C22×C13911yescharacteristic
468C22×D8C22×C13911yescharacteristic
469C22×M16C22×C13911yescharacteristic, complemented
470C23×C8C22×C13911yescharacteristic
471C2×#121—21no—
472C2×#121C22×C13911yescharacteristic
473C2×#121C22×C13911yescharacteristic
474C2×#121C22×C13911yescharacteristic
475C2×#121C22×C13911yescharacteristic, complemented
476C2×#120—21no—
477C2×C4×D4C22×C13911yescharacteristic
478C22×C4⋊C4C22×C13911yescharacteristic
479#469—24no—
480#447—24no—
481#435—24no—
482C2×#106C22×C13911yescharacteristic, complemented
483C2×#106C22×C13911yescharacteristic, complemented
484C2×C4⋊C8C22×C13911yescharacteristic, complemented
485C2×#102—24no—
486C2×#102C22×C13911yescharacteristic
487C2×#102C22×C13911yescharacteristic
488C2×#102C22×C13911yescharacteristic
489C2×#102C22×C13911yescharacteristic
490C2×#102C22×C13911yescharacteristic
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic, complemented
493C2×#102C22×C13911yescharacteristic, complemented
494C2×C22⋊C8C22×C13911yescharacteristic
495C2×C22⋊C8C22×C13911yescharacteristic, complemented
496C2×#97C22×C13911yescharacteristic, complemented
497#396—21no—
498#394—21no—
499#394—21no—
500#392—21no—
501#390C22×C13911yescharacteristic
502#390C22×C13911yescharacteristic
503#390C22×C13911yescharacteristic, complemented
504#389C22×C13911yescharacteristic, complemented
505#386—21no—
506#380C22×C13911yescharacteristic
507#380C22×C13911yescharacteristic, complemented
508#379—21no—
509#340C22×C13911yescharacteristic, complemented
510#340C22×C13911yescharacteristic, complemented
511#340C22×C13911yescharacteristic, complemented
512#340C22×C13911yescharacteristic, complemented
513C25—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4D4×C13911yescharacteristic
526C22×D4C23×C13911yescharacteristic
527C22×D4C23×C13911yescharacteristic
528C22×D4C23×C13911yescharacteristic
529C23×C4—21no—
530C23×C4C23×C13911yescharacteristic
531C23×C4C23×C13911yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8C23×C13911yescharacteristic
545C22×C8C23×C13911yescharacteristic
546C22×C8C23×C13911yescharacteristic
547C22×C8C23×C13911yescharacteristic
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—44no—
557#120—44no—
558C4×D4—22no—
559C4×D4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
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—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C13911yescharacteristic
583C2×C22⋊C4D4×C13911yescharacteristic
584C2×C42C23×C13911yescharacteristic
585#106—22no—
586#106—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C13914yescomplemented
596C22⋊C8—22no—
597C22⋊C8D4×C13914yescomplemented
598#97—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C13911yescharacteristic
613C24C2×D4×C13911yescharacteristic
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
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—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
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—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C13911yescharacteristic
673C22×C4C2×D4×C13911yescharacteristic
674C22×C4C2×D4×C13911yescharacteristic
675C22×C4C2×D4×C13911yescharacteristic
676C22×C4C2×D4×C13912yes—
677C22×C4#41×C13912yes—
678C22×C4C24×C13911yescharacteristic
679D8—44no—
680D8—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8C2×D4×C13912yes—
693C2×C8C2×D4×C13912yes—
694C2×C8C2×D4×C13912yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C13912yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23#121×C13912yes—
764C23AGL(1,ℤ/8)×C13912yes—
765C23AGL(1,ℤ/8)×C13912yes—
766C23C22×D4×C13911yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
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—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—84no—
820C2×C4#121×C13912yes—
821C2×C4C22×D4×C13911yescharacteristic
822C2×C4C22×D4×C13911yescharacteristic
823C2×C4C2×#41×C13911yescharacteristic
824C2×C4C2×#41×C13911yescharacteristic
825C2×C4H(5,𝔽2)×C13911yescharacteristic
826C2×C4H(5,𝔽2)×C13911yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22#469×C13914yescomplemented
867C22C2×#121×C13911yescharacteristic
868C22D42×C13911yescharacteristic
869C22#546×C13911yescharacteristic
870C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
871C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
872C22#576×C13911yescharacteristic
873C22#577×C13911yescharacteristic
874C4—22no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—42no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4#525×C13911yescharacteristic
884C4#538×C13911yescharacteristic
885C4D42×C13911yescharacteristic
886C4#546×C13911yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2#2424×C13911yescharacteristic
893C2C2×#469×C13911yescharacteristic
894C2#3062×C13911yescharacteristic
895C2#3264×C13911yescharacteristic
896C2#3265×C13911yescharacteristic
897C2#3306×C13911yescharacteristic
898C2#3318×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×#469×C139C2semidirect
2. C2×#447×C139C2semidirect
3. C2×#435×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2416×C139C2semidirect
6. #2408×C139C2semidirect
7. #2065×C139C2semidirect
8. #2054×C139C2semidirect
9. #2034×C139C2semidirect
10. #1999×C139C2semidirect
11. #1972×C139C2semidirect
12. #1936×C139C2semidirect
13. #1895×C139C2semidirect
14. #1893×C139C2semidirect
15. #1853×C139C2semidirect
19. C22×M16×C139C22semidirect
25. C2×#121×C139C22semidirect
32. C2×#106×C139C22semidirect
33. C2×#106×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
42. C2×#102×C139C22semidirect
43. C2×#102×C139C22semidirect
45. C2×C22⋊C8×C139C22semidirect
46. C2×#97×C139C22semidirect
53. #390×C139C22semidirect
54. #389×C139C22semidirect
57. #380×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
145. #102×C139D4semidirect
147. C22⋊C8×C139D4semidirect
416. C22×C139#469semidirect
449. #25124C139direct (N × H)
450. C139#25124direct (N × H)
451. C2×#469C2×C139semidirect
452. C2×#447C2×C139semidirect
453. C2×#435C2×C139semidirect
454. C22×#102C2×C139semidirect
455. #2416C2×C139semidirect
456. #2408C2×C139semidirect
457. #2065C2×C139semidirect
458. #2054C2×C139semidirect
459. #2034C2×C139semidirect
460. #1999C2×C139semidirect
461. #1972C2×C139semidirect
462. #1936C2×C139semidirect
463. #1895C2×C139semidirect
464. #1893C2×C139semidirect
465. #1853C2×C139semidirect
469. C22×M16C22×C139semidirect
475. C2×#121C22×C139semidirect
482. C2×#106C22×C139semidirect
483. C2×#106C22×C139semidirect
484. C2×C4⋊C8C22×C139semidirect
492. C2×#102C22×C139semidirect
493. C2×#102C22×C139semidirect
495. C2×C22⋊C8C22×C139semidirect
496. C2×#97C22×C139semidirect
503. #390C22×C139semidirect
504. #389C22×C139semidirect
507. #380C22×C139semidirect
509. #340C22×C139semidirect
510. #340C22×C139semidirect
511. #340C22×C139semidirect
512. #340C22×C139semidirect
595. #102D4×C139semidirect
597. C22⋊C8D4×C139semidirect
866. C22#469×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1392
C2×#447×C1392
C2×#435×C1392
C22×#102×C1392
#2416×C1392
#2408×C1392
#2065×C1392
#2054×C1392
#2034×C1392
#1999×C1392
#1972×C1392
#1936×C1392
#1895×C1392
#1893×C1392
#1853×C1392
#25124139