Finite Group Databasebeta

← C139×#25549 #48020145

Subgroups — C139×#25549 #48020145

Order 35584.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C139C211yesmaximal, characteristic, complemented
2C2×#481×C139C211yesmaximal, characteristic, complemented
3C2×#469×C139C211yesmaximal, characteristic, complemented
4#2414×C139C211yesmaximal, characteristic, complemented
5#2058×C139C211yesmaximal, characteristic, complemented
6#2034×C139C211yesmaximal, characteristic, complemented
7#2023×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1879×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1870×C139C211yesmaximal, characteristic, complemented
13#1864×C139C211yesmaximal, characteristic, complemented
14#1853×C139C211yesmaximal, characteristic, complemented
15#1736×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139—21no—
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19#547×C139—24no—
20#547×C139—24no—
21C2×C4⋊Q8×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×#123×C139—21no—
24C2×C22⋊Q8×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×#117×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2211yescharacteristic
33C22×C4⋊C4×C139C2211yescharacteristic
34#481×C139—24no—
35#469×C139—24no—
36C2×#106×C139C2211yescharacteristic
37C2×#106×C139C2211yescharacteristic
38C2×#106×C139C2211yescharacteristic
39C2×#102×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#390×C139—21no—
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#388×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—44no—
65C2×#41×C139—44no—
66C22×Q8×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C22×D4×C139C2311yescharacteristic
74C23×C4×C139—21no—
75C23×C4×C139—21no—
76C23×C4×C139—21no—
77C23×C4×C139C2311yescharacteristic
78C23×C4×C139C2311yescharacteristic
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C2×D8×C139—41no—
82C2×M16×C139—22no—
83C2×M16×C139—22no—
84C2×M16×C139—41no—
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C4⋊Q8×C139—22no—
90C4⋊Q8×C139—22no—
91#123×C139—28no—
92#123×C139—28no—
93C22⋊Q8×C139—28no—
94#121×C139—22no—
95#121×C139—22no—
96#121×C139—22no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—41no—
101#121×C139D414yescomplemented
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106#117×C139—22no—
107#117×C139—41no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—22no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—22no—
113C2×C4⋊C4×C139—22no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139D411yescharacteristic
116C2×C4⋊C4×C139D414yescomplemented
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C4⋊C4×C139C2311yescharacteristic
122C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
135C2×C42×C139C2311yescharacteristic
136#106×C139—22no—
137#106×C139—22no—
138#106×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—
145C22⋊C8×C139—22no—
146C22⋊C8×C139—22no—
147C22⋊C8×C139—41no—
148#95×C139—21no—
149#95×C139—21no—
150C24×C139—21no—
151C24×C139—21no—
152C24×C139C2×D411yescharacteristic
153C24×C139C2×D411yescharacteristic
154#41×C139—432no—
155C2×Q8×C139—24no—
156C2×Q8×C139—42no—
157C2×Q8×C139—42no—
158C2×D4×C139—22no—
159C2×D4×C139—22no—
160C2×D4×C139—24no—
161C2×D4×C139—24no—
162C2×D4×C139—22no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
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—42no—
175C2×D4×C139—42no—
176C2×D4×C139—42no—
177C2×D4×C139—42no—
178C2×D4×C139—42no—
179C2×D4×C139—42no—
180C2×D4×C139—42no—
181C2×D4×C139—81no—
182C2×D4×C139—81no—
183C2×D4×C139—81no—
184C2×D4×C139C2×D412yes—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—24no—
190C22×C4×C139—24no—
191C22×C4×C139—24no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—42no—
205C22×C4×C139—42no—
206C22×C4×C139—42no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139—42no—
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D412yes—
214C22×C4×C139C2×D412yes—
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2411yescharacteristic
217D8×C139—44no—
218M16×C139—44no—
219C2×C8×C139—21no—
220C2×C8×C139—21no—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139#4112yescomplemented
231C4⋊C4×C139—24no—
232C4⋊C4×C139—24no—
233C4⋊C4×C139—24no—
234C4⋊C4×C139—22no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—81no—
244C4⋊C4×C139C2×D412yes—
245C4⋊C4×C139C2×D412yes—
246C4⋊C4×C139C2×D412yes—
247C4⋊C4×C139#4112yescomplemented
248C22⋊C4×C139—24no—
249C22⋊C4×C139—24no—
250C22⋊C4×C139—22no—
251C22⋊C4×C139—24no—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—81no—
258C22⋊C4×C139—81no—
259C42×C139—21no—
260C42×C139—21no—
261C42×C139—42no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—22no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139#12012yes—
289C23×C139AGL(1,ℤ/8)12yes—
290C23×C139C22×D411yescharacteristic
291Q8×C139—48no—
292D4×C139—28no—
293D4×C139—22no—
294D4×C139—22no—
295D4×C139—48no—
296D4×C139—48no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—84no—
304D4×C139—84no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—22no—
310C2×C4×C139—22no—
311C2×C4×C139—22no—
312C2×C4×C139—22no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—22no—
316C2×C4×C139—22no—
317C2×C4×C139—22no—
318C2×C4×C139—22no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—48no—
324C2×C4×C139—48no—
325C2×C4×C139—48no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139#12012yes—
345C2×C4×C139AGL(1,ℤ/8)12yes—
346C2×C4×C139C22×D411yescharacteristic
347C2×C4×C139C22×D411yescharacteristic
348C2×C4×C139C2×#4111yescharacteristic
349C2×C4×C139C2×#4111yescharacteristic
350C2×C4×C139H(5,𝔽2)11yescharacteristic
351C2×C4×C1392−1+411yescharacteristic
352C8×C139—22no—
353C8×C139—41no—
354C8×C139—41no—
355C8×C139—41no—
356C22×C139—22no—
357C22×C139—22no—
358C22×C139—22no—
359C22×C139—22no—
360C22×C139—22no—
361C22×C139—22no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—41no—
370C22×C139—42no—
371C22×C139—42no—
372C22×C139—42no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139C2×#12011yescharacteristic
385C22×C139#54611yescharacteristic
386C22×C139#54711yescharacteristic
387C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C139#57711yescharacteristic
390C22×C139#57711yescharacteristic
391C4×C139—22no—
392C4×C139—22no—
393C4×C139—41no—
394C4×C139—42no—
395C4×C139—42no—
396C4×C139—42no—
397C4×C139—41no—
398C4×C139—42no—
399C4×C139—81no—
400C4×C139—81no—
401C4×C139#53211yescharacteristic
402C4×C139#53711yescharacteristic
403C4×C139#54611yescharacteristic
404C4×C139#54711yescharacteristic
405C2×C139—42no—
406C2×C139—42no—
407C2×C139—82no—
408C2×C139—161no—
409C2×C139#243011yescharacteristic
410C2×C139#300311yescharacteristic
411C2×C139#301011yescharacteristic
412C2×C139#330611yescharacteristic
413C2×C139#333211yescharacteristic
414C2×C139#334511yescharacteristic
415C2×C139#335411yescharacteristic
416#25549C13911yesmaximal, characteristic, direct product factor, Sylow
417C139#2554911yescharacteristic, direct product factor, Sylow
418C2×#547C2×C13911yescharacteristic, complemented
419C2×#481C2×C13911yescharacteristic, complemented
420C2×#469C2×C13911yescharacteristic, complemented
421#2414C2×C13911yescharacteristic, complemented
422#2058C2×C13911yescharacteristic, complemented
423#2034C2×C13911yescharacteristic, complemented
424#2023C2×C13911yescharacteristic, complemented
425#1999C2×C13911yescharacteristic, complemented
426#1879C2×C13911yescharacteristic, complemented
427#1875C2×C13911yescharacteristic, complemented
428#1874C2×C13911yescharacteristic, complemented
429#1870C2×C13911yescharacteristic, complemented
430#1864C2×C13911yescharacteristic, complemented
431#1853C2×C13911yescharacteristic, complemented
432#1736C2×C13911yescharacteristic, complemented
433C22×#41—21no—
434C22×D8C22×C13911yescharacteristic
435C22×M16C22×C13911yescharacteristic
436#547—24no—
437#547—24no—
438C2×C4⋊Q8C22×C13911yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×C22⋊Q8—21no—
442C2×#121C22×C13911yescharacteristic
443C2×#121C22×C13911yescharacteristic
444C2×#121C22×C13911yescharacteristic
445C2×#121C22×C13911yescharacteristic
446C2×C4×D4C22×C13911yescharacteristic
447C2×C4×D4C22×C13911yescharacteristic
448C2×#117C22×C13911yescharacteristic
449C22×C4⋊C4C22×C13911yescharacteristic
450C22×C4⋊C4C22×C13911yescharacteristic
451#481—24no—
452#469—24no—
453C2×#106C22×C13911yescharacteristic
454C2×#106C22×C13911yescharacteristic
455C2×#106C22×C13911yescharacteristic
456C2×#102C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×#102C22×C13911yescharacteristic
459C2×#102C22×C13911yescharacteristic
460C2×#102C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×C22⋊C8C22×C13911yescharacteristic
463C2×C22⋊C8C22×C13911yescharacteristic
464C2×C22⋊C8C22×C13911yescharacteristic
465#394—21no—
466#392—21no—
467#390—21no—
468#390C22×C13911yescharacteristic
469#389C22×C13911yescharacteristic
470#388—21no—
471#380C22×C13911yescharacteristic
472#340C22×C13911yescharacteristic
473#340C22×C13911yescharacteristic
474#340C22×C13911yescharacteristic
475#340C22×C13911yescharacteristic
476#340C22×C13911yescharacteristic
477#340C22×C13911yescharacteristic
478#336C22×C13911yescharacteristic
479#336C22×C13911yescharacteristic
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C13911yescharacteristic
489C22×D4C23×C13911yescharacteristic
490C22×D4C23×C13911yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C13911yescharacteristic
495C23×C4C23×C13911yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C13911yescharacteristic
503C22×C8C23×C13911yescharacteristic
504C22×C8C23×C13911yescharacteristic
505C22×C8C23×C13911yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C13914yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C13911yescharacteristic
533C2×C4⋊C4D4×C13914yescomplemented
534C2×C4⋊C4C23×C13911yescharacteristic
535C2×C4⋊C4C23×C13911yescharacteristic
536C2×C4⋊C4C23×C13911yescharacteristic
537C2×C4⋊C4C23×C13911yescharacteristic
538C2×C4⋊C4C23×C13911yescharacteristic
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C13911yescharacteristic
550C2×C22⋊C4D4×C13911yescharacteristic
551C2×C42—21no—
552C2×C42C23×C13911yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C13911yescharacteristic
570C24C2×D4×C13911yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C13912yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C13911yescharacteristic
628C22×C4C2×D4×C13911yescharacteristic
629C22×C4C2×D4×C13911yescharacteristic
630C22×C4C2×D4×C13912yes—
631C22×C4C2×D4×C13912yes—
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C24×C13911yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C13912yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C13912yes—
662C4⋊C4C2×D4×C13912yes—
663C4⋊C4C2×D4×C13912yes—
664C4⋊C4#41×C13912yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C13912yes—
706C23AGL(1,ℤ/8)×C13912yes—
707C23C22×D4×C13911yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4#120×C13912yes—
762C2×C4AGL(1,ℤ/8)×C13912yes—
763C2×C4C22×D4×C13911yescharacteristic
764C2×C4C22×D4×C13911yescharacteristic
765C2×C4C2×#41×C13911yescharacteristic
766C2×C4C2×#41×C13911yescharacteristic
767C2×C4H(5,𝔽2)×C13911yescharacteristic
768C2×C42−1+4×C13911yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C13911yescharacteristic
802C22#546×C13911yescharacteristic
803C22#547×C13911yescharacteristic
804C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
805C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
806C22#577×C13911yescharacteristic
807C22#577×C13911yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4#532×C13911yescharacteristic
819C4#537×C13911yescharacteristic
820C4#546×C13911yescharacteristic
821C4#547×C13911yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2#2430×C13911yescharacteristic
827C2#3003×C13911yescharacteristic
828C2#3010×C13911yescharacteristic
829C2#3306×C13911yescharacteristic
830C2#3332×C13911yescharacteristic
831C2#3345×C13911yescharacteristic
832C2#3354×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×#481×C139C2semidirect
3. C2×#469×C139C2semidirect
4. #2414×C139C2semidirect
5. #2058×C139C2semidirect
6. #2034×C139C2semidirect
7. #2023×C139C2semidirect
8. #1999×C139C2semidirect
9. #1879×C139C2semidirect
10. #1875×C139C2semidirect
11. #1874×C139C2semidirect
12. #1870×C139C2semidirect
13. #1864×C139C2semidirect
14. #1853×C139C2semidirect
15. #1736×C139C2semidirect
101. #121×C139D4semidirect
116. C2×C4⋊C4×C139D4semidirect
230. C2×C8×C139#41semidirect
247. C4⋊C4×C139#41semidirect
416. #25549C139direct (N × H)
417. C139#25549direct (N × H)
418. C2×#547C2×C139semidirect
419. C2×#481C2×C139semidirect
420. C2×#469C2×C139semidirect
421. #2414C2×C139semidirect
422. #2058C2×C139semidirect
423. #2034C2×C139semidirect
424. #2023C2×C139semidirect
425. #1999C2×C139semidirect
426. #1879C2×C139semidirect
427. #1875C2×C139semidirect
428. #1874C2×C139semidirect
429. #1870C2×C139semidirect
430. #1864C2×C139semidirect
431. #1853C2×C139semidirect
432. #1736C2×C139semidirect
518. #121D4×C139semidirect
533. C2×C4⋊C4D4×C139semidirect
647. C2×C8#41×C139semidirect
664. C4⋊C4#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×#481×C1392
C2×#469×C1392
#2414×C1392
#2058×C1392
#2034×C1392
#2023×C1392
#1999×C1392
#1879×C1392
#1875×C1392
#1874×C1392
#1870×C1392
#1864×C1392
#1853×C1392
#1736×C1392
#25549139