Finite Group Databasebeta

← C139×#25128 #48019724

Subgroups — C139×#25128 #48019724

Order 35584.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C139C211yesmaximal, characteristic, complemented
2C2×#450×C139C211yesmaximal, characteristic, complemented
3C2×#435×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2417×C139C211yesmaximal, characteristic, complemented
6#2408×C139C211yesmaximal, characteristic
7#2067×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2033×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1973×C139C211yesmaximal, characteristic, complemented
12#1936×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1892×C139C211yesmaximal, characteristic, complemented
15#1852×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic, complemented
20C23×C8×C139C2211yescharacteristic
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic, complemented
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×C4×D4×C139C2211yescharacteristic
27C22×C4⋊C4×C139C2211yescharacteristic
28#468×C139—24no—
29#450×C139—24no—
30#435×C139—24no—
31C2×#107×C139C2211yescharacteristic, complemented
32C2×#107×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34C2×#103×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#102×C139—24no—
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic, complemented
45C2×#97×C139C2211yescharacteristic, complemented
46#398×C139—21no—
47#396×C139—21no—
48#394×C139—21no—
49#392×C139—21no—
50#391×C139C2211yescharacteristic, complemented
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#389×C139C2211yescharacteristic, complemented
54#386×C139—21no—
55#380×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×Q8×C139C2311yescharacteristic
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—22no—
70C22×D4×C139—21no—
71C22×D4×C139—22no—
72C22×D4×C139—41no—
73C22×D4×C139—41no—
74C22×D4×C139D411yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C23×C4×C139—21no—
78C23×C4×C139C2311yescharacteristic
79C23×C4×C139C2311yescharacteristic
80C2×SD16×C139—22no—
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—41no—
85C2×SD16×C139—41no—
86C2×M16×C139—22no—
87C2×M16×C139—22no—
88C2×M16×C139—41no—
89C22×C8×C139—22no—
90C22×C8×C139—22no—
91C22×C8×C139—41no—
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22⋊Q8×C139—22no—
97C22⋊Q8×C139—22no—
98C22⋊Q8×C139—22no—
99C22⋊Q8×C139—41no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—41no—
103#121×C139—41no—
104#120×C139—44no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C2×C4⋊C4×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—41no—
113C2×C4⋊C4×C139D411yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
130C2×C22⋊C4×C139D411yescharacteristic
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133#107×C139—41no—
134C4⋊C8×C139—22no—
135#103×C139—22no—
136#103×C139—41no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139D414yescomplemented
143C22⋊C8×C139—22no—
144C22⋊C8×C139D414yescomplemented
145#97×C139—22no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—42no—
154C24×C139—42no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—81no—
159C24×C139—81no—
160C24×C139C2×D411yescharacteristic
161C24×C139C2×D411yescharacteristic
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×D4×C139—28no—
169C2×D4×C139—22no—
170C2×D4×C139—22no—
171C2×D4×C139—22no—
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—44no—
183C2×D4×C139—44no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—44no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—81no—
193C2×D4×C139—81no—
194C2×D4×C139C2×D412yes—
195C2×D4×C139#4112yes—
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—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—42no—
213C22×C4×C139—42no—
214C22×C4×C139—81no—
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D412yes—
220C22×C4×C139#4112yes—
221C22×C4×C139C2411yescharacteristic
222SD16×C139—44no—
223SD16×C139—44no—
224M16×C139—44no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—44no—
235C2×C8×C139C2×D412yes—
236C2×C8×C139C2×D412yes—
237C2×C8×C139C2×D412yes—
238C4⋊C4×C139—22no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—42no—
249C4⋊C4×C139—42no—
250C4⋊C4×C139—42no—
251C4⋊C4×C139—81no—
252C4⋊C4×C139C2×D412yes—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—81no—
263C22⋊C4×C139—81no—
264C22⋊C4×C139—81no—
265C42×C139—21no—
266C42×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—22no—
274C23×C139—22no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—48no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—84no—
294C23×C139—84no—
295C23×C139—84no—
296C23×C139—84no—
297C23×C139—84no—
298C23×C139—84no—
299C23×C139#12112yes—
300C23×C139AGL(1,ℤ/8)12yes—
301C23×C139#13712yes—
302C23×C139C22×D411yescharacteristic
303Q8×C139—41no—
304Q8×C139—41no—
305Q8×C139—41no—
306Q8×C139—41no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—48no—
312D4×C139—44no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—84no—
318D4×C139—84no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—22no—
322C2×C4×C139—22no—
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—22no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
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—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
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—84no—
357C2×C4×C139#12112yes—
358C2×C4×C139C22×D411yescharacteristic
359C2×C4×C139C22×D411yescharacteristic
360C2×C4×C139C2×#4111yescharacteristic
361C2×C4×C139C2×#4111yescharacteristic
362C2×C4×C139H(5,𝔽2)11yescharacteristic
363C2×C4×C139H(5,𝔽2)11yescharacteristic
364C8×C139—22no—
365C8×C139—22no—
366C8×C139—22no—
367C8×C139—41no—
368C22×C139—22no—
369C22×C139—22no—
370C22×C139—22no—
371C22×C139—22no—
372C22×C139—22no—
373C22×C139—22no—
374C22×C139—41no—
375C22×C139—42no—
376C22×C139—42no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—41no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—42no—
384C22×C139—41no—
385C22×C139—42no—
386C22×C139—41no—
387C22×C139—816no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139#46814yescomplemented
397C22×C139C2×#12111yescharacteristic
398C22×C139D4211yescharacteristic
399C22×C139#54611yescharacteristic
400C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C139C2×#13711yescharacteristic
402C22×C139#57611yescharacteristic
403C22×C139#57711yescharacteristic
404C4×C139—22no—
405C4×C139—41no—
406C4×C139—42no—
407C4×C139—41no—
408C4×C139—41no—
409C4×C139—81no—
410C4×C139—81no—
411C4×C139—81no—
412C4×C139—81no—
413C4×C139—81no—
414C4×C139#52511yescharacteristic
415C4×C139#53811yescharacteristic
416C4×C139D4211yescharacteristic
417C4×C139#54611yescharacteristic
418C2×C139—24no—
419C2×C139—81no—
420C2×C139—82no—
421C2×C139—82no—
422C2×C139#242411yescharacteristic
423C2×C139C2×#46811yescharacteristic
424C2×C139#306211yescharacteristic
425C2×C139#326411yescharacteristic
426C2×C139#326611yescharacteristic
427C2×C139#331011yescharacteristic
428C2×C139#331411yescharacteristic
429#25128C13911yesmaximal, characteristic, direct product factor, Sylow
430C139#2512811yescharacteristic, direct product factor, Sylow
431C2×#468C2×C13911yescharacteristic, complemented
432C2×#450C2×C13911yescharacteristic, complemented
433C2×#435C2×C13911yescharacteristic, complemented
434C22×#102C2×C13911yescharacteristic, complemented
435#2417C2×C13911yescharacteristic, complemented
436#2408C2×C13911yescharacteristic
437#2067C2×C13911yescharacteristic, complemented
438#2055C2×C13911yescharacteristic, complemented
439#2033C2×C13911yescharacteristic, complemented
440#2000C2×C13911yescharacteristic, complemented
441#1973C2×C13911yescharacteristic, complemented
442#1936C2×C13911yescharacteristic, complemented
443#1895C2×C13911yescharacteristic, complemented
444#1892C2×C13911yescharacteristic, complemented
445#1852C2×C13911yescharacteristic, complemented
446C23×D4C22×C13911yescharacteristic
447C22×SD16C22×C13911yescharacteristic
448C22×SD16C22×C13911yescharacteristic
449C22×M16C22×C13911yescharacteristic, complemented
450C23×C8C22×C13911yescharacteristic
451C2×C22⋊Q8C22×C13911yescharacteristic
452C2×C22⋊Q8C22×C13911yescharacteristic, complemented
453C2×#121C22×C13911yescharacteristic
454C2×#121C22×C13911yescharacteristic
455C2×#120—21no—
456C2×C4×D4C22×C13911yescharacteristic
457C22×C4⋊C4C22×C13911yescharacteristic
458#468—24no—
459#450—24no—
460#435—24no—
461C2×#107C22×C13911yescharacteristic, complemented
462C2×#107C22×C13911yescharacteristic, complemented
463C2×C4⋊C8C22×C13911yescharacteristic, complemented
464C2×#103C22×C13911yescharacteristic, complemented
465C2×#103C22×C13911yescharacteristic, complemented
466C2×#102—24no—
467C2×#102C22×C13911yescharacteristic
468C2×#102C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×#102C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic
473C2×C22⋊C8C22×C13911yescharacteristic
474C2×C22⋊C8C22×C13911yescharacteristic, complemented
475C2×#97C22×C13911yescharacteristic, complemented
476#398—21no—
477#396—21no—
478#394—21no—
479#392—21no—
480#391C22×C13911yescharacteristic, complemented
481#390C22×C13911yescharacteristic
482#390C22×C13911yescharacteristic
483#389C22×C13911yescharacteristic, complemented
484#386—21no—
485#380—21no—
486#380C22×C13911yescharacteristic
487#380C22×C13911yescharacteristic, complemented
488#379—21no—
489#340C22×C13911yescharacteristic, complemented
490#340C22×C13911yescharacteristic, complemented
491#340C22×C13911yescharacteristic, complemented
492#340C22×C13911yescharacteristic, complemented
493C25—21no—
494C22×Q8C23×C13911yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C13911yescharacteristic
505C22×D4C23×C13911yescharacteristic
506C22×D4C23×C13911yescharacteristic
507C23×C4—21no—
508C23×C4C23×C13911yescharacteristic
509C23×C4C23×C13911yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C13911yescharacteristic
523C22×C8C23×C13911yescharacteristic
524C22×C8C23×C13911yescharacteristic
525C22×C8C23×C13911yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C13911yescharacteristic
544C2×C4⋊C4C23×C13911yescharacteristic
545C2×C4⋊C4C23×C13911yescharacteristic
546C2×C4⋊C4C23×C13911yescharacteristic
547C2×C4⋊C4C23×C13911yescharacteristic
548C2×C4⋊C4C23×C13911yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C13911yescharacteristic
560C2×C22⋊C4D4×C13911yescharacteristic
561C2×C42C23×C13911yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C13914yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C13914yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C13911yescharacteristic
591C24C2×D4×C13911yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C13912yes—
625C2×D4#41×C13912yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C13911yescharacteristic
646C22×C4C2×D4×C13911yescharacteristic
647C22×C4C2×D4×C13911yescharacteristic
648C22×C4C2×D4×C13911yescharacteristic
649C22×C4C2×D4×C13912yes—
650C22×C4#41×C13912yes—
651C22×C4C24×C13911yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C13912yes—
666C2×C8C2×D4×C13912yes—
667C2×C8C2×D4×C13912yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C13912yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C13912yes—
730C23AGL(1,ℤ/8)×C13912yes—
731C23#137×C13912yes—
732C23C22×D4×C13911yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4#121×C13912yes—
788C2×C4C22×D4×C13911yescharacteristic
789C2×C4C22×D4×C13911yescharacteristic
790C2×C4C2×#41×C13911yescharacteristic
791C2×C4C2×#41×C13911yescharacteristic
792C2×C4H(5,𝔽2)×C13911yescharacteristic
793C2×C4H(5,𝔽2)×C13911yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#468×C13914yescomplemented
827C22C2×#121×C13911yescharacteristic
828C22D42×C13911yescharacteristic
829C22#546×C13911yescharacteristic
830C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
831C22C2×#137×C13911yescharacteristic
832C22#576×C13911yescharacteristic
833C22#577×C13911yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4#525×C13911yescharacteristic
845C4#538×C13911yescharacteristic
846C4D42×C13911yescharacteristic
847C4#546×C13911yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2#2424×C13911yescharacteristic
853C2C2×#468×C13911yescharacteristic
854C2#3062×C13911yescharacteristic
855C2#3264×C13911yescharacteristic
856C2#3266×C13911yescharacteristic
857C2#3310×C13911yescharacteristic
858C2#3314×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2408×C139C2
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×#468×C139C2semidirect
2. C2×#450×C139C2semidirect
3. C2×#435×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2417×C139C2semidirect
7. #2067×C139C2semidirect
8. #2055×C139C2semidirect
9. #2033×C139C2semidirect
10. #2000×C139C2semidirect
11. #1973×C139C2semidirect
12. #1936×C139C2semidirect
13. #1895×C139C2semidirect
14. #1892×C139C2semidirect
15. #1852×C139C2semidirect
19. C22×M16×C139C22semidirect
22. C2×C22⋊Q8×C139C22semidirect
31. C2×#107×C139C22semidirect
32. C2×#107×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
34. C2×#103×C139C22semidirect
35. C2×#103×C139C22semidirect
44. C2×C22⋊C8×C139C22semidirect
45. C2×#97×C139C22semidirect
50. #391×C139C22semidirect
53. #389×C139C22semidirect
57. #380×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
142. #102×C139D4semidirect
144. C22⋊C8×C139D4semidirect
396. C22×C139#468semidirect
429. #25128C139direct (N × H)
430. C139#25128direct (N × H)
431. C2×#468C2×C139semidirect
432. C2×#450C2×C139semidirect
433. C2×#435C2×C139semidirect
434. C22×#102C2×C139semidirect
435. #2417C2×C139semidirect
437. #2067C2×C139semidirect
438. #2055C2×C139semidirect
439. #2033C2×C139semidirect
440. #2000C2×C139semidirect
441. #1973C2×C139semidirect
442. #1936C2×C139semidirect
443. #1895C2×C139semidirect
444. #1892C2×C139semidirect
445. #1852C2×C139semidirect
449. C22×M16C22×C139semidirect
452. C2×C22⋊Q8C22×C139semidirect
461. C2×#107C22×C139semidirect
462. C2×#107C22×C139semidirect
463. C2×C4⋊C8C22×C139semidirect
464. C2×#103C22×C139semidirect
465. C2×#103C22×C139semidirect
474. C2×C22⋊C8C22×C139semidirect
475. C2×#97C22×C139semidirect
480. #391C22×C139semidirect
483. #389C22×C139semidirect
487. #380C22×C139semidirect
489. #340C22×C139semidirect
490. #340C22×C139semidirect
491. #340C22×C139semidirect
492. #340C22×C139semidirect
572. #102D4×C139semidirect
574. C22⋊C8D4×C139semidirect
826. C22#468×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1392
C2×#450×C1392
C2×#435×C1392
C22×#102×C1392
#2417×C1392
#2408×C1392
#2067×C1392
#2055×C1392
#2033×C1392
#2000×C1392
#1973×C1392
#1936×C1392
#1895×C1392
#1892×C1392
#1852×C1392
#25128139