Finite Group Databasebeta

← C139×#24901 #48019497

Subgroups — C139×#24901 #48019497

Order 35584.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C139C211yesmaximal, characteristic
2C2×C4×SD16×C139C211yesmaximal, characteristic, complemented
3#2423×C139C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C139C211yesmaximal, characteristic
5#2094×C139C211yesmaximal, characteristic, complemented
6#2077×C139C211yesmaximal, characteristic, complemented
7#2055×C139C211yesmaximal, characteristic, complemented
8#2035×C139C211yesmaximal, characteristic, complemented
9#1934×C139C211yesmaximal, characteristic, complemented
10#1923×C139C211yesmaximal, characteristic, complemented
11#1880×C139C211yesmaximal, characteristic, complemented
12#1877×C139C211yesmaximal, characteristic, complemented
13#1864×C139C211yesmaximal, characteristic, complemented
14#1802×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C2×C22⋊Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic, complemented
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C22×C22⋊C4×C139—21no—
24#450×C139—24no—
25C4×SD16×C139—24no—
26C2×#106×C139C2211yescharacteristic, complemented
27C2×#106×C139C2211yescharacteristic, complemented
28C2×C4⋊C8×C139C2211yescharacteristic, complemented
29C2×#103×C139C2211yescharacteristic, complemented
30C2×#103×C139C2211yescharacteristic, complemented
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×C22⋊C8×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C4×C8×C139C2211yescharacteristic, complemented
40#399×C139—21no—
41#398×C139—21no—
42#391×C139C2211yescharacteristic, complemented
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#389×C139C2211yescharacteristic, complemented
46#388×C139—21no—
47#387×C139—21no—
48#386×C139—21no—
49#386×C139—21no—
50#384×C139C2211yescharacteristic, complemented
51#380×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#379×C139—21no—
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic, complemented
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#336×C139C2211yescharacteristic, complemented
60#336×C139C2211yescharacteristic, complemented
61C25×C139—21no—
62C22×Q8×C139C2311yescharacteristic
63C22×D4×C139—22no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—41no—
69C22×D4×C139—41no—
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C23×C4×C139—21no—
73C23×C4×C139—21no—
74C23×C4×C139C2311yescharacteristic
75C2×SD16×C139—22no—
76C2×SD16×C139—22no—
77C2×SD16×C139—22no—
78C2×SD16×C139—22no—
79C2×SD16×C139—41no—
80C2×SD16×C139D414yes—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85C22⋊Q8×C139—22no—
86C22⋊Q8×C139—41no—
87C4×Q8×C139—22no—
88C4×Q8×C139—41no—
89C4×D4×C139—22no—
90C4×D4×C139—22no—
91C4×D4×C139—41no—
92C4×D4×C139—41no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139—21no—
97C2×C4⋊C4×C139—21no—
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—44no—
113C2×C22⋊C4×C139D411yescharacteristic
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C42×C139—21no—
116C2×C42×C139C2311yescharacteristic
117C2×C42×C139C2311yescharacteristic
118#106×C139—22no—
119#106×C139—41no—
120C4⋊C8×C139—41no—
121#103×C139—22no—
122#103×C139—41no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—22no—
128#102×C139—41no—
129C22⋊C8×C139—22no—
130C22⋊C8×C139—41no—
131C4×C8×C139—22no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139D411yescharacteristic
138#95×C139D411yescharacteristic
139C24×C139—21no—
140C24×C139—24no—
141C24×C139—21no—
142C24×C139—42no—
143C24×C139—42no—
144C24×C139—42no—
145C24×C139—42no—
146C24×C139—81no—
147C24×C139—81no—
148C24×C139C2×D411yescharacteristic
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139—21no—
152C2×Q8×C139—21no—
153C2×Q8×C139—21no—
154C2×Q8×C139C2×D412yes—
155C2×D4×C139—24no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—44no—
167C2×D4×C139—44no—
168C2×D4×C139—44no—
169C2×D4×C139—44no—
170C2×D4×C139C2×D412yes—
171C2×D4×C139#4112yes—
172C2×D4×C139#4112yes—
173C2×D4×C139#4112yes—
174C22×C4×C139—21no—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—42no—
187C22×C4×C139—42no—
188C22×C4×C139—42no—
189C22×C4×C139—42no—
190C22×C4×C139—81no—
191C22×C4×C139—81no—
192C22×C4×C139C2×D411yescharacteristic
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2411yescharacteristic
198SD16×C139—28no—
199SD16×C139—44no—
200C2×C8×C139—21no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139C2×D412yes—
212C4⋊C4×C139—21no—
213C4⋊C4×C139—21no—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—42no—
223C4⋊C4×C139—42no—
224C4⋊C4×C139—42no—
225C4⋊C4×C139—81no—
226C4⋊C4×C139—81no—
227C22⋊C4×C139—41no—
228C22⋊C4×C139—42no—
229C22⋊C4×C139—42no—
230C22⋊C4×C139—42no—
231C22⋊C4×C139—42no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—81no—
235C22⋊C4×C139—81no—
236C22⋊C4×C139—81no—
237C22⋊C4×C139SD1614yescomplemented
238C42×C139—21no—
239C42×C139—21no—
240C42×C139—21no—
241C42×C139—21no—
242C42×C139—42no—
243C23×C139—21no—
244C23×C139—22no—
245C23×C139—21no—
246C23×C139—22no—
247C23×C139—22no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—22no—
253C23×C139—48no—
254C23×C139—48no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139—41no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—84no—
266C23×C139—84no—
267C23×C139—84no—
268C23×C139—84no—
269C23×C139—84no—
270C23×C139C2×SD1612yes—
271C23×C139C22×D411yescharacteristic
272Q8×C139—22no—
273Q8×C139—22no—
274Q8×C139—41no—
275Q8×C139—41no—
276D4×C139—22no—
277D4×C139—22no—
278D4×C139—22no—
279D4×C139—22no—
280D4×C139—22no—
281D4×C139—48no—
282D4×C139—41no—
283D4×C139—41no—
284D4×C139#12314yes—
285C2×C4×C139—21no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—22no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—41no—
300C2×C4×C139—41no—
301C2×C4×C139—41no—
302C2×C4×C139—41no—
303C2×C4×C139—41no—
304C2×C4×C139—41no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
309C2×C4×C139—41no—
310C2×C4×C139—41no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—84no—
321C2×C4×C139—84no—
322C2×C4×C139C2×SD1612yes—
323C2×C4×C139C2×SD1612yes—
324C2×C4×C139C22×D411yescharacteristic
325C2×C4×C139C2×#4111yescharacteristic
326C2×C4×C139C2×#4111yescharacteristic
327C2×C4×C139C2×#4111yescharacteristic
328C2×C4×C139H(5,𝔽2)11yescharacteristic
329C2×C4×C139H(5,𝔽2)11yescharacteristic
330C8×C139—22no—
331C8×C139—41no—
332C8×C139—41no—
333C8×C139—41no—
334C22×C139—22no—
335C22×C139—24no—
336C22×C139—22no—
337C22×C139—22no—
338C22×C139—42no—
339C22×C139—41no—
340C22×C139—42no—
341C22×C139—41no—
342C22×C139—41no—
343C22×C139—42no—
344C22×C139—42no—
345C22×C139—42no—
346C22×C139—41no—
347C22×C139—42no—
348C22×C139—42no—
349C22×C139—42no—
350C22×C139—42no—
351C22×C139—816no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139#52511yescharacteristic
357C22×C139D4211yescharacteristic
358C22×C139#54611yescharacteristic
359C22×C139C22×SD1611yescharacteristic
360C22×C139#57511yescharacteristic
361C22×C139#57611yescharacteristic
362C22×C139#57711yescharacteristic
363C4×C139—22no—
364C4×C139—22no—
365C4×C139—41no—
366C4×C139—42no—
367C4×C139—41no—
368C4×C139—41no—
369C4×C139—81no—
370C4×C139—81no—
371C4×C139—81no—
372C4×C139—81no—
373C4×C139—81no—
374C4×C139C2×#12311yescharacteristic
375C4×C139#53811yescharacteristic
376C4×C139#54611yescharacteristic
377C4×C139#55111yescharacteristic
378C2×C139—42no—
379C2×C139—44no—
380C2×C139—82no—
381C2×C139#241811yescharacteristic
382C2×C139#310111yescharacteristic
383C2×C139#311811yescharacteristic
384C2×C139#326811yescharacteristic
385C2×C139D4×SD1611yescharacteristic
386C2×C139#329511yescharacteristic
387C2×C139#332311yescharacteristic
388#24901C13911yesmaximal, characteristic, direct product factor, Sylow
389C139#2490111yescharacteristic, direct product factor, Sylow
390C2×#450C2×C13911yescharacteristic
391C2×C4×SD16C2×C13911yescharacteristic, complemented
392#2423C2×C13911yescharacteristic, complemented
393D4×C22⋊C4C2×C13911yescharacteristic
394#2094C2×C13911yescharacteristic, complemented
395#2077C2×C13911yescharacteristic, complemented
396#2055C2×C13911yescharacteristic, complemented
397#2035C2×C13911yescharacteristic, complemented
398#1934C2×C13911yescharacteristic, complemented
399#1923C2×C13911yescharacteristic, complemented
400#1880C2×C13911yescharacteristic, complemented
401#1877C2×C13911yescharacteristic, complemented
402#1864C2×C13911yescharacteristic, complemented
403#1802C2×C13911yescharacteristic, complemented
404#1786C2×C13911yescharacteristic
405C23×D4C22×C13911yescharacteristic
406C22×SD16C22×C13911yescharacteristic
407C22×SD16C22×C13911yescharacteristic
408C2×C22⋊Q8C22×C13911yescharacteristic
409C2×C4×Q8C22×C13911yescharacteristic, complemented
410C2×C4×D4C22×C13911yescharacteristic
411C2×C4×D4C22×C13911yescharacteristic
412C22×C22⋊C4—21no—
413#450—24no—
414C4×SD16—24no—
415C2×#106C22×C13911yescharacteristic, complemented
416C2×#106C22×C13911yescharacteristic, complemented
417C2×C4⋊C8C22×C13911yescharacteristic, complemented
418C2×#103C22×C13911yescharacteristic, complemented
419C2×#103C22×C13911yescharacteristic, complemented
420C2×#102C22×C13911yescharacteristic
421C2×#102C22×C13911yescharacteristic
422C2×#102C22×C13911yescharacteristic
423C2×#102C22×C13911yescharacteristic
424C2×#102C22×C13911yescharacteristic
425C2×#102C22×C13911yescharacteristic
426C2×C22⋊C8C22×C13911yescharacteristic
427C2×C22⋊C8C22×C13911yescharacteristic
428C2×C4×C8C22×C13911yescharacteristic, complemented
429#399—21no—
430#398—21no—
431#391C22×C13911yescharacteristic, complemented
432#390C22×C13911yescharacteristic
433#390C22×C13911yescharacteristic
434#389C22×C13911yescharacteristic, complemented
435#388—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#384C22×C13911yescharacteristic, complemented
440#380C22×C13911yescharacteristic
441#380C22×C13911yescharacteristic
442#379—21no—
443C4×C22⋊C4C22×C13911yescharacteristic
444#340C22×C13911yescharacteristic, complemented
445#340C22×C13911yescharacteristic, complemented
446#340C22×C13911yescharacteristic, complemented
447#340C22×C13911yescharacteristic, complemented
448#336C22×C13911yescharacteristic, complemented
449#336C22×C13911yescharacteristic, complemented
450C25—21no—
451C22×Q8C23×C13911yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C13911yescharacteristic
460C22×D4C23×C13911yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C13911yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C13914yes—
470C22×C8C23×C13911yescharacteristic
471C22×C8C23×C13911yescharacteristic
472C22×C8C23×C13911yescharacteristic
473C22×C8C23×C13911yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C13911yescharacteristic
488C2×C4⋊C4C23×C13911yescharacteristic
489C2×C4⋊C4C23×C13911yescharacteristic
490C2×C4⋊C4C23×C13911yescharacteristic
491C2×C4⋊C4C23×C13911yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C13911yescharacteristic
503C2×C22⋊C4D4×C13911yescharacteristic
504C2×C42—21no—
505C2×C42C23×C13911yescharacteristic
506C2×C42C23×C13911yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C13911yescharacteristic
527#95D4×C13911yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C13911yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C13912yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C13912yes—
560C2×D4#41×C13912yes—
561C2×D4#41×C13912yes—
562C2×D4#41×C13912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C13911yescharacteristic
582C22×C4C2×D4×C13911yescharacteristic
583C22×C4C2×D4×C13911yescharacteristic
584C22×C4C2×D4×C13911yescharacteristic
585C22×C4C2×D4×C13911yescharacteristic
586C22×C4C24×C13911yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C13912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C13914yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C13912yes—
660C23C22×D4×C13911yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C13914yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C13912yes—
712C2×C4C2×SD16×C13912yes—
713C2×C4C22×D4×C13911yescharacteristic
714C2×C4C2×#41×C13911yescharacteristic
715C2×C4C2×#41×C13911yescharacteristic
716C2×C4C2×#41×C13911yescharacteristic
717C2×C4H(5,𝔽2)×C13911yescharacteristic
718C2×C4H(5,𝔽2)×C13911yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#525×C13911yescharacteristic
746C22D42×C13911yescharacteristic
747C22#546×C13911yescharacteristic
748C22C22×SD16×C13911yescharacteristic
749C22#575×C13911yescharacteristic
750C22#576×C13911yescharacteristic
751C22#577×C13911yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C13911yescharacteristic
764C4#538×C13911yescharacteristic
765C4#546×C13911yescharacteristic
766C4#551×C13911yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#2418×C13911yescharacteristic
771C2#3101×C13911yescharacteristic
772C2#3118×C13911yescharacteristic
773C2#3268×C13911yescharacteristic
774C2D4×SD16×C13911yescharacteristic
775C2#3295×C13911yescharacteristic
776C2#3323×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC23×D4×C139C22
LCSG ▷ C22×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×C4×SD16×C139C2semidirect
3. #2423×C139C2semidirect
5. #2094×C139C2semidirect
6. #2077×C139C2semidirect
7. #2055×C139C2semidirect
8. #2035×C139C2semidirect
9. #1934×C139C2semidirect
10. #1923×C139C2semidirect
11. #1880×C139C2semidirect
12. #1877×C139C2semidirect
13. #1864×C139C2semidirect
14. #1802×C139C2semidirect
20. C2×C4×Q8×C139C22semidirect
26. C2×#106×C139C22semidirect
27. C2×#106×C139C22semidirect
28. C2×C4⋊C8×C139C22semidirect
29. C2×#103×C139C22semidirect
30. C2×#103×C139C22semidirect
39. C2×C4×C8×C139C22semidirect
42. #391×C139C22semidirect
45. #389×C139C22semidirect
50. #384×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #336×C139C22semidirect
60. #336×C139C22semidirect
237. C22⋊C4×C139SD16semidirect
388. #24901C139direct (N × H)
389. C139#24901direct (N × H)
391. C2×C4×SD16C2×C139semidirect
392. #2423C2×C139semidirect
394. #2094C2×C139semidirect
395. #2077C2×C139semidirect
396. #2055C2×C139semidirect
397. #2035C2×C139semidirect
398. #1934C2×C139semidirect
399. #1923C2×C139semidirect
400. #1880C2×C139semidirect
401. #1877C2×C139semidirect
402. #1864C2×C139semidirect
403. #1802C2×C139semidirect
409. C2×C4×Q8C22×C139semidirect
415. C2×#106C22×C139semidirect
416. C2×#106C22×C139semidirect
417. C2×C4⋊C8C22×C139semidirect
418. C2×#103C22×C139semidirect
419. C2×#103C22×C139semidirect
428. C2×C4×C8C22×C139semidirect
431. #391C22×C139semidirect
434. #389C22×C139semidirect
439. #384C22×C139semidirect
444. #340C22×C139semidirect
445. #340C22×C139semidirect
446. #340C22×C139semidirect
447. #340C22×C139semidirect
448. #336C22×C139semidirect
449. #336C22×C139semidirect
626. C22⋊C4SD16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1392
C2×C4×SD16×C1392
#2423×C1392
D4×C22⋊C4×C1392
#2094×C1392
#2077×C1392
#2055×C1392
#2035×C1392
#1934×C1392
#1923×C1392
#1880×C1392
#1877×C1392
#1864×C1392
#1802×C1392
#1786×C1392
#24901139