Finite Group Databasebeta

← C139×#22442 #48017038

Subgroups — C139×#22442 #48017038

Order 35584.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic
2C2×#442×C139C211yesmaximal, characteristic, complemented
3C2×C4×D8×C139C211yesmaximal, characteristic, complemented
4#2339×C139C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
6#1973×C139C211yesmaximal, characteristic, complemented
7#1968×C139C211yesmaximal, characteristic, complemented
8#1879×C139C211yesmaximal, characteristic, complemented
9#1879×C139C211yesmaximal, characteristic, complemented
10#1877×C139C211yesmaximal, characteristic, complemented
11#1877×C139C211yesmaximal, characteristic, complemented
12#1809×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15#1753×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139—24no—
19C2×AGL(1,ℤ/8)×C139—24no—
20C2×AGL(1,ℤ/8)×C139C418yescomplemented
21C22×SD16×C139C2211yescharacteristic
22C22×SD16×C139C2211yescharacteristic
23C22×D8×C139C2211yescharacteristic
24C22×D8×C139C2211yescharacteristic
25C22×M16×C139C2211yescharacteristic
26C2×C4×D4×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic, complemented
29C2×C4×D4×C139C2211yescharacteristic, complemented
30C22×C22⋊C4×C139—21no—
31#442×C139—24no—
32C4×D8×C139—24no—
33C2×#107×C139C2211yescharacteristic, complemented
34C2×#106×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic, complemented
42C2×#102×C139C2211yescharacteristic, complemented
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×#97×C139C2211yescharacteristic, complemented
45C2×C4×C8×C139C2211yescharacteristic, complemented
46#391×C139C2211yescharacteristic, complemented
47#391×C139C2211yescharacteristic, complemented
48#390×C139C2211yescharacteristic
49#390×C139C2211yescharacteristic
50#386×C139—21no—
51#386×C139—21no—
52#386×C139—21no—
53#386×C139—21no—
54#381×C139—21no—
55#380×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#379×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59C2×#95×C139—21no—
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63#336×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—22no—
77C22×D4×C139—41no—
78C22×D4×C139—41no—
79C22×D4×C139C2×C414yescomplemented
80C22×D4×C139C2311yescharacteristic
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139—21no—
87C23×C4×C139—21no—
88C23×C4×C139C2311yescharacteristic
89AGL(1,ℤ/8)×C139—232no—
90C2×SD16×C139—22no—
91C2×SD16×C139—22no—
92C2×SD16×C139—22no—
93C2×SD16×C139—22no—
94C2×SD16×C139C2×C414yescomplemented
95C2×SD16×C139C2×C414yescomplemented
96C2×D8×C139—22no—
97C2×D8×C139—22no—
98C2×D8×C139C2×C414yes—
99C2×D8×C139C2×C414yescomplemented
100C2×D8×C139D414yes—
101C2×D8×C139D414yes—
102C2×M16×C139—22no—
103C2×M16×C139—22no—
104C2×M16×C139C2×C414yescomplemented
105C22×C8×C139C2311yescharacteristic
106C22×C8×C139C2311yescharacteristic
107C22×C8×C139C2311yescharacteristic
108C22×C8×C139C2311yescharacteristic
109C4×D4×C139—22no—
110C4×D4×C139—22no—
111C4×D4×C139—22no—
112C4×D4×C139—22no—
113C4×D4×C139—41no—
114C4×D4×C139—41no—
115C4×D4×C139—41no—
116C4×D4×C139—41no—
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
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—44no—
132C2×C22⋊C4×C139D411yescharacteristic
133C2×C22⋊C4×C139D411yescharacteristic
134C2×C42×C139C2311yescharacteristic
135C2×C42×C139C2311yescharacteristic
136#107×C139—22no—
137#106×C139—22no—
138#103×C139—41no—
139#103×C139—41no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139—41no—
145#102×C139—41no—
146C22⋊C8×C139—22no—
147#97×C139—22no—
148C4×C8×C139—22no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154#95×C139—21no—
155#95×C139D411yescharacteristic
156#95×C139D411yescharacteristic
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—24no—
161C24×C139—42no—
162C24×C139—42no—
163C24×C139—42no—
164C24×C139—42no—
165C24×C139—81no—
166C24×C139—81no—
167C24×C139C2×D411yescharacteristic
168#41×C139—28no—
169#41×C139—44no—
170#41×C139—44no—
171#41×C139—44no—
172C2×Q8×C139—21no—
173C2×Q8×C139—21no—
174C2×Q8×C139—21no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139C22×C412yes—
178C2×D4×C139—28no—
179C2×D4×C139—24no—
180C2×D4×C139—24no—
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—21no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—44no—
193C2×D4×C139—44no—
194C2×D4×C139—44no—
195C2×D4×C139—42no—
196C2×D4×C139—42no—
197C2×D4×C139—42no—
198C2×D4×C139—42no—
199C2×D4×C139C22×C412yes—
200C2×D4×C139C22×C412yes—
201C2×D4×C139C22×C412yes—
202C2×D4×C139C2×D412yes—
203C2×D4×C139C2×D412yes—
204C2×D4×C139C2×D412yes—
205C2×D4×C139C2×D412yes—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—24no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—42no—
217C22×C4×C139—42no—
218C22×C4×C139—42no—
219C22×C4×C139—42no—
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—81no—
227C22×C4×C139—81no—
228C22×C4×C139—81no—
229C22×C4×C139—81no—
230C22×C4×C139C22×C412yes—
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D411yescharacteristic
235C22×C4×C139C2×D411yescharacteristic
236C22×C4×C139#4112yes—
237C22×C4×C139C2411yescharacteristic
238SD16×C139—28no—
239SD16×C139—28no—
240D8×C139—28no—
241D8×C139C22⋊C4116yescomplemented
242M16×C139—28no—
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×C139C22×C412yes—
252C2×C8×C139C22×C412yes—
253C2×C8×C139C2×D412yes—
254C2×C8×C139C2×D412yes—
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—
263C22⋊C4×C139—22no—
264C22⋊C4×C139—41no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—42no—
268C22⋊C4×C139—42no—
269C22⋊C4×C139—42no—
270C22⋊C4×C139—42no—
271C22⋊C4×C139—42no—
272C22⋊C4×C139—81no—
273C22⋊C4×C139—81no—
274C22⋊C4×C139—81no—
275C42×C139—21no—
276C42×C139—21no—
277C42×C139—21no—
278C42×C139—21no—
279C23×C139—22no—
280C23×C139—22no—
281C23×C139—22no—
282C23×C139—22no—
283C23×C139—22no—
284C23×C139—22no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—22no—
292C23×C139—48no—
293C23×C139—48no—
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—41no—
308C23×C139—84no—
309C23×C139—84no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139—84no—
313C23×C139C4×D412yes—
314C23×C139C22×D411yescharacteristic
315Q8×C139—22no—
316Q8×C139—22no—
317Q8×C139—41no—
318Q8×C139—41no—
319D4×C139—22no—
320D4×C139—22no—
321D4×C139—22no—
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×C139C2×C22⋊C414yes—
332D4×C139C2×C22⋊C414yescomplemented
333C2×C4×C139—21no—
334C2×C4×C139—21no—
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—22no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—48no—
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—84no—
367C2×C4×C139—84no—
368C2×C4×C139—84no—
369C2×C4×C139—84no—
370C2×C4×C139C4×D412yes—
371C2×C4×C139AGL(1,ℤ/8)12yescomplemented
372C2×C4×C139C23×C411yescharacteristic
373C2×C4×C139C22×D411yescharacteristic
374C2×C4×C139C22×D411yescharacteristic
375C2×C4×C139C2×#4111yescharacteristic
376C2×C4×C139H(5,𝔽2)11yescharacteristic
377C2×C4×C139H(5,𝔽2)11yescharacteristic
378C8×C139—22no—
379C8×C139—41no—
380C8×C139—41no—
381C8×C139C2×C22⋊C414yescomplemented
382C22×C139—22no—
383C22×C139—24no—
384C22×C139—24no—
385C22×C139—22no—
386C22×C139—22no—
387C22×C139—42no—
388C22×C139—42no—
389C22×C139—42no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—41no—
394C22×C139—41no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—42no—
398C22×C139—41no—
399C22×C139—42no—
400C22×C139—42no—
401C22×C139—41no—
402C22×C139—42no—
403C22×C139—42no—
404C22×C139—42no—
405C22×C139—42no—
406C22×C139—816no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139C2×C4×D411yescharacteristic
412C22×C139D4211yescharacteristic
413C22×C139D4211yescharacteristic
414C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C139#57511yescharacteristic
416C22×C139#57611yescharacteristic
417C22×C139#57711yescharacteristic
418C4×C139—22no—
419C4×C139—22no—
420C4×C139—42no—
421C4×C139—41no—
422C4×C139—41no—
423C4×C139—41no—
424C4×C139—81no—
425C4×C139—81no—
426C4×C139—81no—
427C4×C139—81no—
428C4×C139C22×C22⋊C411yescharacteristic
429C4×C139#51811yescharacteristic
430C4×C139#54611yescharacteristic
431C4×C139#54611yescharacteristic
432C2×C139—42no—
433C2×C139—44no—
434C2×C139—44no—
435C2×C139—82no—
436C2×C139D4×C22⋊C411yescharacteristic
437C2×C139C4×AGL(1,ℤ/8)11yescharacteristic
438C2×C139#294611yescharacteristic
439C2×C139#326411yescharacteristic
440C2×C139#326711yescharacteristic
441C2×C139#327211yescharacteristic
442C2×C139#327311yescharacteristic
443#22442C13911yesmaximal, characteristic, direct product factor, Sylow
444C139#2244211yescharacteristic, direct product factor, Sylow
445C22×AGL(1,ℤ/8)C2×C13911yescharacteristic
446C2×#442C2×C13911yescharacteristic, complemented
447C2×C4×D8C2×C13911yescharacteristic, complemented
448#2339C2×C13911yescharacteristic, complemented
449D4×C22⋊C4C2×C13911yescharacteristic, complemented
450#1973C2×C13911yescharacteristic, complemented
451#1968C2×C13911yescharacteristic, complemented
452#1879C2×C13911yescharacteristic, complemented
453#1879C2×C13911yescharacteristic, complemented
454#1877C2×C13911yescharacteristic, complemented
455#1877C2×C13911yescharacteristic, complemented
456#1809C2×C13911yescharacteristic, complemented
457#1788C2×C13911yescharacteristic, complemented
458#1786C2×C13911yescharacteristic, complemented
459#1753C2×C13911yescharacteristic, complemented
460C22×#41C22×C13911yescharacteristic
461C23×D4C22×C13911yescharacteristic
462C2×AGL(1,ℤ/8)—24no—
463C2×AGL(1,ℤ/8)—24no—
464C2×AGL(1,ℤ/8)C4×C13918yescomplemented
465C22×SD16C22×C13911yescharacteristic
466C22×SD16C22×C13911yescharacteristic
467C22×D8C22×C13911yescharacteristic
468C22×D8C22×C13911yescharacteristic
469C22×M16C22×C13911yescharacteristic
470C2×C4×D4C22×C13911yescharacteristic
471C2×C4×D4C22×C13911yescharacteristic
472C2×C4×D4C22×C13911yescharacteristic, complemented
473C2×C4×D4C22×C13911yescharacteristic, complemented
474C22×C22⋊C4—21no—
475#442—24no—
476C4×D8—24no—
477C2×#107C22×C13911yescharacteristic, complemented
478C2×#106C22×C13911yescharacteristic, complemented
479C2×#103C22×C13911yescharacteristic, complemented
480C2×#103C22×C13911yescharacteristic, complemented
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×#102C22×C13911yescharacteristic
484C2×#102C22×C13911yescharacteristic
485C2×#102C22×C13911yescharacteristic, complemented
486C2×#102C22×C13911yescharacteristic, complemented
487C2×C22⋊C8C22×C13911yescharacteristic
488C2×#97C22×C13911yescharacteristic, complemented
489C2×C4×C8C22×C13911yescharacteristic, complemented
490#391C22×C13911yescharacteristic, complemented
491#391C22×C13911yescharacteristic, complemented
492#390C22×C13911yescharacteristic
493#390C22×C13911yescharacteristic
494#386—21no—
495#386—21no—
496#386—21no—
497#386—21no—
498#381—21no—
499#380C22×C13911yescharacteristic
500#380C22×C13911yescharacteristic
501#379—21no—
502C4×C22⋊C4C22×C13911yescharacteristic
503C2×#95—21no—
504#340C22×C13911yescharacteristic, complemented
505#340C22×C13911yescharacteristic, complemented
506#336C22×C13911yescharacteristic, complemented
507#336C22×C13911yescharacteristic, complemented
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×C4×C13914yescomplemented
515C22×Q8C23×C13911yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×C4×C13914yescomplemented
524C22×D4C23×C13911yescharacteristic
525C22×D4C23×C13911yescharacteristic
526C22×D4C23×C13911yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C23×C13911yescharacteristic
533AGL(1,ℤ/8)—232no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16C2×C4×C13914yescomplemented
539C2×SD16C2×C4×C13914yescomplemented
540C2×D8—22no—
541C2×D8—22no—
542C2×D8C2×C4×C13914yes—
543C2×D8C2×C4×C13914yescomplemented
544C2×D8D4×C13914yes—
545C2×D8D4×C13914yes—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16C2×C4×C13914yescomplemented
549C22×C8C23×C13911yescharacteristic
550C22×C8C23×C13911yescharacteristic
551C22×C8C23×C13911yescharacteristic
552C22×C8C23×C13911yescharacteristic
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C2×C4⋊C4C23×C13911yescharacteristic
562C2×C4⋊C4C23×C13911yescharacteristic
563C2×C4⋊C4C23×C13911yescharacteristic
564C2×C4⋊C4C23×C13911yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
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—44no—
576C2×C22⋊C4D4×C13911yescharacteristic
577C2×C22⋊C4D4×C13911yescharacteristic
578C2×C42C23×C13911yescharacteristic
579C2×C42C23×C13911yescharacteristic
580#107—22no—
581#106—22no—
582#103—41no—
583#103—41no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590C22⋊C8—22no—
591#97—22no—
592C4×C8—22no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95D4×C13911yescharacteristic
600#95D4×C13911yescharacteristic
601C24—21no—
602C24—21no—
603C24—21no—
604C24—24no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—81no—
610C24—81no—
611C24C2×D4×C13911yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C22×C4×C13912yes—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
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—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C13912yes—
644C2×D4C22×C4×C13912yes—
645C2×D4C22×C4×C13912yes—
646C2×D4C2×D4×C13912yes—
647C2×D4C2×D4×C13912yes—
648C2×D4C2×D4×C13912yes—
649C2×D4C2×D4×C13912yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4—81no—
674C22×C4C22×C4×C13912yes—
675C22×C4C2×D4×C13911yescharacteristic
676C22×C4C2×D4×C13911yescharacteristic
677C22×C4C2×D4×C13911yescharacteristic
678C22×C4C2×D4×C13911yescharacteristic
679C22×C4C2×D4×C13911yescharacteristic
680C22×C4#41×C13912yes—
681C22×C4C24×C13911yescharacteristic
682SD16—28no—
683SD16—28no—
684D8—28no—
685D8C22⋊C4×C139116yescomplemented
686M16—28no—
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×C8C22×C4×C13912yes—
696C2×C8C22×C4×C13912yes—
697C2×C8C2×D4×C13912yes—
698C2×C8C2×D4×C13912yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—81no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
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—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23C4×D4×C13912yes—
758C23C22×D4×C13911yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊C4×C13914yes—
776D4C2×C22⋊C4×C13914yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
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—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4C4×D4×C13912yes—
815C2×C4AGL(1,ℤ/8)×C13912yescomplemented
816C2×C4C23×C4×C13911yescharacteristic
817C2×C4C22×D4×C13911yescharacteristic
818C2×C4C22×D4×C13911yescharacteristic
819C2×C4C2×#41×C13911yescharacteristic
820C2×C4H(5,𝔽2)×C13911yescharacteristic
821C2×C4H(5,𝔽2)×C13911yescharacteristic
822C8—22no—
823C8—41no—
824C8—41no—
825C8C2×C22⋊C4×C13914yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×C4×D4×C13911yescharacteristic
856C22D42×C13911yescharacteristic
857C22D42×C13911yescharacteristic
858C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
859C22#575×C13911yescharacteristic
860C22#576×C13911yescharacteristic
861C22#577×C13911yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4C22×C22⋊C4×C13911yescharacteristic
873C4#518×C13911yescharacteristic
874C4#546×C13911yescharacteristic
875C4#546×C13911yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊C4×C13911yescharacteristic
881C2C4×AGL(1,ℤ/8)×C13911yescharacteristic
882C2#2946×C13911yescharacteristic
883C2#3264×C13911yescharacteristic
884C2#3267×C13911yescharacteristic
885C2#3272×C13911yescharacteristic
886C2#3273×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC22×AGL(1,ℤ/8)×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#442×C139C2semidirect
3. C2×C4×D8×C139C2semidirect
4. #2339×C139C2semidirect
5. D4×C22⋊C4×C139C2semidirect
6. #1973×C139C2semidirect
7. #1968×C139C2semidirect
8. #1879×C139C2semidirect
9. #1879×C139C2semidirect
10. #1877×C139C2semidirect
11. #1877×C139C2semidirect
12. #1809×C139C2semidirect
13. #1788×C139C2semidirect
14. #1786×C139C2semidirect
15. #1753×C139C2semidirect
20. C2×AGL(1,ℤ/8)×C139C4semidirect
28. C2×C4×D4×C139C22semidirect
29. C2×C4×D4×C139C22semidirect
33. C2×#107×C139C22semidirect
34. C2×#106×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
41. C2×#102×C139C22semidirect
42. C2×#102×C139C22semidirect
44. C2×#97×C139C22semidirect
45. C2×C4×C8×C139C22semidirect
46. #391×C139C22semidirect
47. #391×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #336×C139C22semidirect
63. #336×C139C22semidirect
70. C2×#41×C139C2×C4semidirect
79. C22×D4×C139C2×C4semidirect
94. C2×SD16×C139C2×C4semidirect
95. C2×SD16×C139C2×C4semidirect
99. C2×D8×C139C2×C4semidirect
104. C2×M16×C139C2×C4semidirect
241. D8×C139C22⋊C4semidirect
332. D4×C139C2×C22⋊C4semidirect
371. C2×C4×C139AGL(1,ℤ/8)semidirect
381. C8×C139C2×C22⋊C4semidirect
443. #22442C139direct (N × H)
444. C139#22442direct (N × H)
446. C2×#442C2×C139semidirect
447. C2×C4×D8C2×C139semidirect
448. #2339C2×C139semidirect
449. D4×C22⋊C4C2×C139semidirect
450. #1973C2×C139semidirect
451. #1968C2×C139semidirect
452. #1879C2×C139semidirect
453. #1879C2×C139semidirect
454. #1877C2×C139semidirect
455. #1877C2×C139semidirect
456. #1809C2×C139semidirect
457. #1788C2×C139semidirect
458. #1786C2×C139semidirect
459. #1753C2×C139semidirect
464. C2×AGL(1,ℤ/8)C4×C139semidirect
472. C2×C4×D4C22×C139semidirect
473. C2×C4×D4C22×C139semidirect
477. C2×#107C22×C139semidirect
478. C2×#106C22×C139semidirect
479. C2×#103C22×C139semidirect
480. C2×#103C22×C139semidirect
485. C2×#102C22×C139semidirect
486. C2×#102C22×C139semidirect
488. C2×#97C22×C139semidirect
489. C2×C4×C8C22×C139semidirect
490. #391C22×C139semidirect
491. #391C22×C139semidirect
504. #340C22×C139semidirect
505. #340C22×C139semidirect
506. #336C22×C139semidirect
507. #336C22×C139semidirect
514. C2×#41C2×C4×C139semidirect
523. C22×D4C2×C4×C139semidirect
538. C2×SD16C2×C4×C139semidirect
539. C2×SD16C2×C4×C139semidirect
543. C2×D8C2×C4×C139semidirect
548. C2×M16C2×C4×C139semidirect
685. D8C22⋊C4×C139semidirect
776. D4C2×C22⋊C4×C139semidirect
815. C2×C4AGL(1,ℤ/8)×C139semidirect
825. C8C2×C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1392
C2×#442×C1392
C2×C4×D8×C1392
#2339×C1392
D4×C22⋊C4×C1392
#1973×C1392
#1968×C1392
#1879×C1392
#1877×C1392
#1809×C1392
#1788×C1392
#1786×C1392
#1753×C1392
#22442139