Finite Group Databasebeta

← C139×#25076 #48019672

Subgroups — C139×#25076 #48019672

Order 35584.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C139C211yesmaximal, characteristic, complemented
2C2×#459×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2433×C139C211yesmaximal, characteristic, complemented
6#2361×C139C211yesmaximal, characteristic, complemented
7#2067×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2041×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1925×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1874×C139C211yesmaximal, characteristic, complemented
15#1850×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic, complemented
20C23×C8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#127×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×#120×C139—21no—
27C2×C4×D4×C139—21no—
28C2×C4×D4×C139C2211yescharacteristic, complemented
29C22×C4⋊C4×C139C2211yescharacteristic
30#466×C139—24no—
31#459×C139—24no—
32#447×C139—24no—
33C2×#107×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35C2×C4⋊C8×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×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic, complemented
47C2×C22⋊C8×C139C2211yescharacteristic
48#392×C139—21no—
49#392×C139—21no—
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic, complemented
53#389×C139C2211yescharacteristic, complemented
54#388×C139—21no—
55#386×C139—21no—
56#385×C139—21no—
57C4×C4⋊C4×C139C2211yescharacteristic, complemented
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#336×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—22no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—22no—
75C22×D4×C139—41no—
76C22×D4×C139—41no—
77C22×D4×C139C2311yescharacteristic
78C22×D4×C139C2311yescharacteristic
79C22×D4×C139C2311yescharacteristic
80C22×D4×C139C2311yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139—21no—
83C23×C4×C139C2311yescharacteristic
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—22no—
87C2×D8×C139—22no—
88C2×D8×C139—22no—
89C2×D8×C139—22no—
90C2×D8×C139—41no—
91C2×D8×C139—41no—
92C2×D8×C139—41no—
93C22×C8×C139—22no—
94C22×C8×C139—22no—
95C22×C8×C139—41no—
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99C22×C8×C139C2311yescharacteristic
100#127×C139—22no—
101#127×C139—22no—
102#127×C139—41no—
103#127×C139—41no—
104#121×C139—22no—
105#121×C139—22no—
106#121×C139—22no—
107#121×C139D414yescomplemented
108#120×C139—44no—
109#120×C139—44no—
110C4×D4×C139—22no—
111C4×D4×C139—41no—
112C4×D4×C139—44no—
113C2×C4⋊C4×C139—22no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×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×C139D411yescharacteristic
131C2×C22⋊C4×C139D411yescharacteristic
132C2×C42×C139—21no—
133C2×C42×C139C2311yescharacteristic
134C2×C42×C139C2311yescharacteristic
135#107×C139—22no—
136C4⋊C8×C139—22no—
137C4⋊C8×C139—41no—
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—22no—
145#102×C139—22no—
146#102×C139—41no—
147#102×C139D414yescomplemented
148C22⋊C8×C139—22no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139D411yescharacteristic
152#95×C139D411yescharacteristic
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139—21no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—42no—
161C24×C139—42no—
162C24×C139—81no—
163C24×C139—81no—
164C24×C139C2×D411yescharacteristic
165C2×D4×C139—28no—
166C2×D4×C139—24no—
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—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—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—44no—
189C2×D4×C139—44no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—44no—
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—42no—
200C2×D4×C139—42no—
201C2×D4×C139—42no—
202C2×D4×C139—42no—
203C2×D4×C139—42no—
204C2×D4×C139—42no—
205C2×D4×C139—42no—
206C2×D4×C139—42no—
207C2×D4×C139—81no—
208C2×D4×C139—81no—
209C2×D4×C139—81no—
210C2×D4×C139—81no—
211C2×D4×C139C2×D412yes—
212C2×D4×C139C2×D412yes—
213C2×D4×C139#4112yes—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
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×C139C2×D411yescharacteristic
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D412yes—
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139#4112yes—
235C22×C4×C139C2411yescharacteristic
236D8×C139—44no—
237D8×C139—44no—
238D8×C139—44no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
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—44no—
251C2×C8×C139C2×D412yes—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139—21no—
255C4⋊C4×C139—21no—
256C4⋊C4×C139—21no—
257C4⋊C4×C139—21no—
258C4⋊C4×C139—42no—
259C4⋊C4×C139—42no—
260C4⋊C4×C139C2×D412yes—
261C4⋊C4×C139C2×D412yes—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—24no—
264C22⋊C4×C139—42no—
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—81no—
272C22⋊C4×C139D814yescomplemented
273C42×C139—21no—
274C42×C139—21no—
275C42×C139—21no—
276C42×C139—21no—
277C42×C139—42no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—21no—
282C23×C139—22no—
283C23×C139—22no—
284C23×C139—22no—
285C23×C139—48no—
286C23×C139—41no—
287C23×C139—41no—
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—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—84no—
312C23×C139—84no—
313C23×C139—84no—
314C23×C139—84no—
315C23×C139—84no—
316C23×C139—84no—
317C23×C139#12112yes—
318C23×C139C2×D812yes—
319C23×C139AGL(1,ℤ/8)12yes—
320C23×C139C22×D411yescharacteristic
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×C139—41no—
332D4×C139—41no—
333D4×C139—41no—
334D4×C139—41no—
335D4×C139—41no—
336D4×C139—41no—
337D4×C139—41no—
338D4×C139—41no—
339D4×C139—84no—
340D4×C139—84no—
341D4×C139—84no—
342D4×C139—84no—
343D4×C139—84no—
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—22no—
351C2×C4×C139—22no—
352C2×C4×C139—22no—
353C2×C4×C139—22no—
354C2×C4×C139—22no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
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—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—84no—
373C2×C4×C139—84no—
374C2×C4×C139#12112yes—
375C2×C4×C139C2×D812yes—
376C2×C4×C139C2×D812yes—
377C2×C4×C139C22×D411yescharacteristic
378C2×C4×C139C22×D411yescharacteristic
379C2×C4×C139C2×#4111yescharacteristic
380C2×C4×C139C2×#4111yescharacteristic
381C2×C4×C139H(5,𝔽2)11yescharacteristic
382C2×C4×C139H(5,𝔽2)11yescharacteristic
383C8×C139—22no—
384C8×C139—41no—
385C8×C139—41no—
386C8×C139—41no—
387C22×C139—22no—
388C22×C139—22no—
389C22×C139—22no—
390C22×C139—22no—
391C22×C139—22no—
392C22×C139—22no—
393C22×C139—42no—
394C22×C139—42no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—42no—
398C22×C139—42no—
399C22×C139—42no—
400C22×C139—42no—
401C22×C139—42no—
402C22×C139—816no—
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—81no—
417C22×C139—81no—
418C22×C139—81no—
419C22×C139—81no—
420C22×C139—81no—
421C22×C139—81no—
422C22×C139#45914yescomplemented
423C22×C139C2×#12111yescharacteristic
424C22×C139D4211yescharacteristic
425C22×C139#54611yescharacteristic
426C22×C139C22×D811yescharacteristic
427C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C139#57611yescharacteristic
429C22×C139#57711yescharacteristic
430C4×C139—22no—
431C4×C139—22no—
432C4×C139—22no—
433C4×C139—41no—
434C4×C139—42no—
435C4×C139—42no—
436C4×C139—41no—
437C4×C139—81no—
438C4×C139—81no—
439C4×C139#52511yescharacteristic
440C4×C139#53811yescharacteristic
441C4×C139D4211yescharacteristic
442C4×C139#54611yescharacteristic
443C2×C139—24no—
444C2×C139—82no—
445C2×C139—82no—
446C2×C139—82no—
447C2×C139—161no—
448C2×C139#242411yescharacteristic
449C2×C139C2×#45911yescharacteristic
450C2×C139#304511yescharacteristic
451C2×C139#326511yescharacteristic
452C2×C139D4×D811yescharacteristic
453C2×C139#329411yescharacteristic
454C2×C139#331811yescharacteristic
455#25076C13911yesmaximal, characteristic, direct product factor, Sylow
456C139#2507611yescharacteristic, direct product factor, Sylow
457C2×#466C2×C13911yescharacteristic, complemented
458C2×#459C2×C13911yescharacteristic, complemented
459C2×#447C2×C13911yescharacteristic, complemented
460C22×#102C2×C13911yescharacteristic, complemented
461#2433C2×C13911yescharacteristic, complemented
462#2361C2×C13911yescharacteristic, complemented
463#2067C2×C13911yescharacteristic, complemented
464#2054C2×C13911yescharacteristic, complemented
465#2041C2×C13911yescharacteristic, complemented
466#2011C2×C13911yescharacteristic, complemented
467#1982C2×C13911yescharacteristic, complemented
468#1925C2×C13911yescharacteristic, complemented
469#1879C2×C13911yescharacteristic, complemented
470#1874C2×C13911yescharacteristic, complemented
471#1850C2×C13911yescharacteristic, complemented
472C23×D4C22×C13911yescharacteristic
473C22×D8C22×C13911yescharacteristic
474C22×D8C22×C13911yescharacteristic
475C22×D8C22×C13911yescharacteristic, complemented
476C23×C8C22×C13911yescharacteristic
477C2×#127C22×C13911yescharacteristic
478C2×#127C22×C13911yescharacteristic
479C2×#121C22×C13911yescharacteristic
480C2×#121C22×C13911yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C13911yescharacteristic, complemented
485C22×C4⋊C4C22×C13911yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C13911yescharacteristic, complemented
490C2×C4⋊C8C22×C13911yescharacteristic, complemented
491C2×C4⋊C8C22×C13911yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C13911yescharacteristic
494C2×#102C22×C13911yescharacteristic
495C2×#102C22×C13911yescharacteristic
496C2×#102C22×C13911yescharacteristic
497C2×#102C22×C13911yescharacteristic
498C2×#102C22×C13911yescharacteristic
499C2×#102C22×C13911yescharacteristic, complemented
500C2×#102C22×C13911yescharacteristic, complemented
501C2×#102C22×C13911yescharacteristic, complemented
502C2×#102C22×C13911yescharacteristic, complemented
503C2×C22⋊C8C22×C13911yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C13911yescharacteristic
507#390C22×C13911yescharacteristic
508#390C22×C13911yescharacteristic, complemented
509#389C22×C13911yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C13911yescharacteristic, complemented
514C4×C22⋊C4C22×C13911yescharacteristic
515#340C22×C13911yescharacteristic, complemented
516#340C22×C13911yescharacteristic, complemented
517#336C22×C13911yescharacteristic, complemented
518#336C22×C13911yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C13911yescharacteristic
534C22×D4C23×C13911yescharacteristic
535C22×D4C23×C13911yescharacteristic
536C22×D4C23×C13911yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C13911yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C13911yescharacteristic
553C22×C8C23×C13911yescharacteristic
554C22×C8C23×C13911yescharacteristic
555C22×C8C23×C13911yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C13914yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C13911yescharacteristic
574C2×C4⋊C4C23×C13911yescharacteristic
575C2×C4⋊C4C23×C13911yescharacteristic
576C2×C4⋊C4C23×C13911yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C13911yescharacteristic
587C2×C22⋊C4D4×C13911yescharacteristic
588C2×C42—21no—
589C2×C42C23×C13911yescharacteristic
590C2×C42C23×C13911yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C13914yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C13911yescharacteristic
608#95D4×C13911yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C13911yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
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—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C13912yes—
668C2×D4C2×D4×C13912yes—
669C2×D4#41×C13912yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C13911yescharacteristic
685C22×C4C2×D4×C13911yescharacteristic
686C22×C4C2×D4×C13911yescharacteristic
687C22×C4C2×D4×C13912yes—
688C22×C4C2×D4×C13911yescharacteristic
689C22×C4C2×D4×C13911yescharacteristic
690C22×C4#41×C13912yes—
691C22×C4C24×C13911yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C13912yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C13912yes—
717C4⋊C4C2×D4×C13912yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C13914yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
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—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C13912yes—
774C23C2×D8×C13912yes—
775C23AGL(1,ℤ/8)×C13912yes—
776C23C22×D4×C13911yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C13912yes—
831C2×C4C2×D8×C13912yes—
832C2×C4C2×D8×C13912yes—
833C2×C4C22×D4×C13911yescharacteristic
834C2×C4C22×D4×C13911yescharacteristic
835C2×C4C2×#41×C13911yescharacteristic
836C2×C4C2×#41×C13911yescharacteristic
837C2×C4H(5,𝔽2)×C13911yescharacteristic
838C2×C4H(5,𝔽2)×C13911yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C13914yescomplemented
879C22C2×#121×C13911yescharacteristic
880C22D42×C13911yescharacteristic
881C22#546×C13911yescharacteristic
882C22C22×D8×C13911yescharacteristic
883C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
884C22#576×C13911yescharacteristic
885C22#577×C13911yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—42no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4#525×C13911yescharacteristic
896C4#538×C13911yescharacteristic
897C4D42×C13911yescharacteristic
898C4#546×C13911yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2#2424×C13911yescharacteristic
905C2C2×#459×C13911yescharacteristic
906C2#3045×C13911yescharacteristic
907C2#3265×C13911yescharacteristic
908C2D4×D8×C13911yescharacteristic
909C2#3294×C13911yescharacteristic
910C2#3318×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
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
1. C2×#466×C139C2semidirect
2. C2×#459×C139C2semidirect
3. C2×#447×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2433×C139C2semidirect
6. #2361×C139C2semidirect
7. #2067×C139C2semidirect
8. #2054×C139C2semidirect
9. #2041×C139C2semidirect
10. #2011×C139C2semidirect
11. #1982×C139C2semidirect
12. #1925×C139C2semidirect
13. #1879×C139C2semidirect
14. #1874×C139C2semidirect
15. #1850×C139C2semidirect
19. C22×D8×C139C22semidirect
28. C2×C4×D4×C139C22semidirect
33. C2×#107×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
35. C2×C4⋊C8×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
46. C2×#102×C139C22semidirect
52. #390×C139C22semidirect
53. #389×C139C22semidirect
57. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
107. #121×C139D4semidirect
147. #102×C139D4semidirect
272. C22⋊C4×C139D8semidirect
422. C22×C139#459semidirect
455. #25076C139direct (N × H)
456. C139#25076direct (N × H)
457. C2×#466C2×C139semidirect
458. C2×#459C2×C139semidirect
459. C2×#447C2×C139semidirect
460. C22×#102C2×C139semidirect
461. #2433C2×C139semidirect
462. #2361C2×C139semidirect
463. #2067C2×C139semidirect
464. #2054C2×C139semidirect
465. #2041C2×C139semidirect
466. #2011C2×C139semidirect
467. #1982C2×C139semidirect
468. #1925C2×C139semidirect
469. #1879C2×C139semidirect
470. #1874C2×C139semidirect
471. #1850C2×C139semidirect
475. C22×D8C22×C139semidirect
484. C2×C4×D4C22×C139semidirect
489. C2×#107C22×C139semidirect
490. C2×C4⋊C8C22×C139semidirect
491. C2×C4⋊C8C22×C139semidirect
499. C2×#102C22×C139semidirect
500. C2×#102C22×C139semidirect
501. C2×#102C22×C139semidirect
502. C2×#102C22×C139semidirect
508. #390C22×C139semidirect
509. #389C22×C139semidirect
513. C4×C4⋊C4C22×C139semidirect
515. #340C22×C139semidirect
516. #340C22×C139semidirect
517. #336C22×C139semidirect
518. #336C22×C139semidirect
563. #121D4×C139semidirect
603. #102D4×C139semidirect
728. C22⋊C4D8×C139semidirect
878. C22#459×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1392
C2×#459×C1392
C2×#447×C1392
C22×#102×C1392
#2433×C1392
#2361×C1392
#2067×C1392
#2054×C1392
#2041×C1392
#2011×C1392
#1982×C1392
#1925×C1392
#1879×C1392
#1874×C1392
#1850×C1392
#25076139