Finite Group Databasebeta

← C139×#24389 #48018985

Subgroups — C139×#24389 #48018985

Order 35584.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C139C211yesmaximal, characteristic
2C2×#470×C139C211yesmaximal, characteristic, complemented
3C2×#468×C139C211yesmaximal, characteristic, complemented
4C2×#452×C139C211yesmaximal, characteristic, complemented
5C2×#407×C139C211yesmaximal, characteristic, complemented
6#2848×C139C211yesmaximal, characteristic, complemented
7#2036×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#2001×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1894×C139C211yesmaximal, characteristic, complemented
13#1873×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C24×C4×C139C2211yescharacteristic
18C22×Q16×C139C2211yescharacteristic, complemented
19C22×SD16×C139C2211yescharacteristic, complemented
20C22×M16×C139C2211yescharacteristic
21C22×M16×C139C2211yescharacteristic
22#525×C139—24no—
23#525×C139—24no—
24C2×#123×C139—21no—
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×C22⋊Q8×C139C2211yescharacteristic
27C2×C22⋊Q8×C139C2211yescharacteristic
28C2×C22⋊Q8×C139C2211yescharacteristic
29C2×C22⋊Q8×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×#121×C139C2211yescharacteristic
32C2×#120×C139—21no—
33C2×C4×D4×C139—21no—
34C2×C4×D4×C139—21no—
35C2×#117×C139C2211yescharacteristic
36#470×C139—24no—
37#468×C139—24no—
38#452×C139—24no—
39C2×#107×C139C2211yescharacteristic, complemented
40C2×#106×C139C2211yescharacteristic, complemented
41C2×#103×C139C2211yescharacteristic, complemented
42C2×#103×C139C2211yescharacteristic, complemented
43C2×#103×C139C2211yescharacteristic, complemented
44C2×#103×C139C2211yescharacteristic, complemented
45C2×#103×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic, complemented
47C2×#102×C139C2211yescharacteristic, complemented
48C2×#102×C139C2211yescharacteristic, complemented
49#407×C139—24no—
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54#385×C139—21no—
55#385×C139—21no—
56#385×C139—21no—
57#380×C139C2211yescharacteristic
58#380×C139C2211yescharacteristic
59#380×C139C2211yescharacteristic
60#379×C139—21no—
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×C139C2211yescharacteristic, complemented
65C25×C139D411yescharacteristic
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C22×Q8×C139C2311yescharacteristic
73C22×Q8×C139C2311yescharacteristic
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139C2311yescharacteristic
78C23×C4×C139—22no—
79C23×C4×C139—21no—
80C23×C4×C139—22no—
81C23×C4×C139—22no—
82C23×C4×C139—22no—
83C23×C4×C139—41no—
84C23×C4×C139—41no—
85C23×C4×C139D411yescharacteristic
86C23×C4×C139D411yescharacteristic
87C23×C4×C139D411yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C23×C4×C139C2311yescharacteristic
90C23×C4×C139C2311yescharacteristic
91C2×Q16×C139—22no—
92C2×Q16×C139—22no—
93C2×Q16×C139—41no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—41no—
97C2×M16×C139—22no—
98C2×M16×C139—22no—
99C2×M16×C139—22no—
100C2×M16×C139—22no—
101C2×M16×C139—41no—
102C2×M16×C139—41no—
103C22×C8×C139C2311yescharacteristic
104C22×C8×C139C2311yescharacteristic
105C22×C8×C139C2311yescharacteristic
106C22×C8×C139C2311yescharacteristic
107#123×C139—28no—
108C22⋊Q8×C139—22no—
109C22⋊Q8×C139—22no—
110C22⋊Q8×C139—22no—
111C22⋊Q8×C139—22no—
112C22⋊Q8×C139—22no—
113C22⋊Q8×C139—22no—
114C22⋊Q8×C139—22no—
115C22⋊Q8×C139—41no—
116C22⋊Q8×C139—41no—
117C22⋊Q8×C139D414yes—
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139D414yes—
122#120×C139—28no—
123C4×D4×C139—28no—
124C4×D4×C139—28no—
125#117×C139—22no—
126#117×C139—22no—
127C2×C4⋊C4×C139—21no—
128C2×C4⋊C4×C139—21no—
129C2×C4⋊C4×C139—21no—
130C2×C4⋊C4×C139—21no—
131C2×C4⋊C4×C139—21no—
132C2×C4⋊C4×C139C2311yescharacteristic
133C2×C4⋊C4×C139C2311yescharacteristic
134C2×C4⋊C4×C139C2311yescharacteristic
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C4⋊C4×C139C2311yescharacteristic
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139—21no—
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—21no—
144C2×C22⋊C4×C139—21no—
145C2×C22⋊C4×C139—21no—
146C2×C22⋊C4×C139—21no—
147C2×C22⋊C4×C139—21no—
148C2×C42×C139—21no—
149#107×C139—22no—
150#106×C139—22no—
151#103×C139—22no—
152#103×C139—22no—
153#103×C139—22no—
154#103×C139—22no—
155#103×C139—41no—
156#102×C139—22no—
157#102×C139—22no—
158#102×C139—41no—
159C22⋊C8×C139—22no—
160C22⋊C8×C139—22no—
161C22⋊C8×C139—22no—
162C22⋊C8×C139D414yescomplemented
163#95×C139—21no—
164#95×C139—21no—
165#95×C139—21no—
166C24×C139—22no—
167C24×C139—22no—
168C24×C139—22no—
169C24×C139—21no—
170C24×C139—41no—
171C24×C139—41no—
172C24×C139—41no—
173C24×C139—41no—
174C24×C139C2×D411yescharacteristic
175C24×C139C2×D411yescharacteristic
176C24×C139C2×D411yescharacteristic
177#41×C139—44no—
178#41×C139—44no—
179#41×C139—44no—
180#41×C139—44no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139—21no—
192C2×Q8×C139C2×D412yes—
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—24no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
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×C139C2×D412yes—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—24no—
217C22×C4×C139—22no—
218C22×C4×C139—22no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—22no—
223C22×C4×C139—22no—
224C22×C4×C139—22no—
225C22×C4×C139—22no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—41no—
237C22×C4×C139—41no—
238C22×C4×C139—41no—
239C22×C4×C139—44no—
240C22×C4×C139—44no—
241C22×C4×C139—44no—
242C22×C4×C139—44no—
243C22×C4×C139—42no—
244C22×C4×C139—42no—
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D412yes—
248C22×C4×C139C2×D412yes—
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2×D412yes—
251C22×C4×C139#4112yes—
252C22×C4×C139C2411yescharacteristic
253Q16×C139—44no—
254SD16×C139—44no—
255M16×C139—44no—
256M16×C139—44no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139C2×D412yes—
268C2×C8×C139C2×D412yes—
269C4⋊C4×C139—24no—
270C4⋊C4×C139—24no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—42no—
280C4⋊C4×C139—42no—
281C4⋊C4×C139—42no—
282C4⋊C4×C139C2×D412yes—
283C4⋊C4×C139C2×D412yes—
284C22⋊C4×C139—24no—
285C22⋊C4×C139—24no—
286C22⋊C4×C139—24no—
287C22⋊C4×C139—24no—
288C22⋊C4×C139—24no—
289C22⋊C4×C139—42no—
290C22⋊C4×C139—42no—
291C22⋊C4×C139—42no—
292C22⋊C4×C139—42no—
293C22⋊C4×C139—42no—
294C22⋊C4×C139—42no—
295C42×C139—24no—
296C23×C139—21no—
297C23×C139—21no—
298C23×C139—21no—
299C23×C139—21no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—21no—
307C23×C139—21no—
308C23×C139—21no—
309C23×C139—21no—
310C23×C139—21no—
311C23×C139—21no—
312C23×C139—21no—
313C23×C139—21no—
314C23×C139—22no—
315C23×C139—44no—
316C23×C139—44no—
317C23×C139—44no—
318C23×C139—44no—
319C23×C139—44no—
320C23×C139—44no—
321C23×C139—44no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139#12012yes—
329C23×C139#12112yes—
330C23×C139#13712yes—
331C23×C139C22×D411yescharacteristic
332Q8×C139—22no—
333Q8×C139—22no—
334Q8×C139—41no—
335Q8×C139—41no—
336Q8×C139—41no—
337Q8×C139—41no—
338Q8×C139—41no—
339Q8×C139—41no—
340D4×C139—22no—
341D4×C139—22no—
342D4×C139—48no—
343D4×C139—48no—
344D4×C139—48no—
345D4×C139—41no—
346D4×C139—41no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—22no—
352C2×C4×C139—22no—
353C2×C4×C139—22no—
354C2×C4×C139—22no—
355C2×C4×C139—22no—
356C2×C4×C139—22no—
357C2×C4×C139—22no—
358C2×C4×C139—22no—
359C2×C4×C139—22no—
360C2×C4×C139—22no—
361C2×C4×C139—21no—
362C2×C4×C139—22no—
363C2×C4×C139—21no—
364C2×C4×C139—21no—
365C2×C4×C139—44no—
366C2×C4×C139—44no—
367C2×C4×C139—44no—
368C2×C4×C139—48no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—41no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
382C2×C4×C139—41no—
383C2×C4×C139—41no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139#12012yes—
392C2×C4×C139#12112yes—
393C2×C4×C139C22×D411yescharacteristic
394C2×C4×C139C22×D411yescharacteristic
395C2×C4×C139C22×D411yescharacteristic
396C2×C4×C139C2×#4111yescharacteristic
397C2×C4×C139H(5,𝔽2)11yescharacteristic
398C2×C4×C139H(5,𝔽2)11yescharacteristic
399C8×C139—22no—
400C8×C139—22no—
401C8×C139—41no—
402C8×C139—41no—
403C22×C139—22no—
404C22×C139—22no—
405C22×C139—22no—
406C22×C139—22no—
407C22×C139—22no—
408C22×C139—22no—
409C22×C139—22no—
410C22×C139—22no—
411C22×C139—22no—
412C22×C139—416no—
413C22×C139—41no—
414C22×C139—41no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—41no—
418C22×C139—41no—
419C22×C139—41no—
420C22×C139—41no—
421C22×C139—41no—
422C22×C139—41no—
423C22×C139—41no—
424C22×C139—41no—
425C22×C139—42no—
426C22×C139—42no—
427C22×C139—42no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139—81no—
431C22×C139—81no—
432C22×C139C2×#12011yescharacteristic
433C22×C139C2×#12111yescharacteristic
434C22×C139#53411yescharacteristic
435C22×C139C2×#13711yescharacteristic
436C22×C139#57511yescharacteristic
437C22×C139#57511yescharacteristic
438C22×C139#57511yescharacteristic
439C4×C139—22no—
440C4×C139—22no—
441C4×C139—41no—
442C4×C139—42no—
443C4×C139—42no—
444C4×C139—42no—
445C4×C139—81no—
446C4×C139—81no—
447C4×C139—81no—
448C4×C139—81no—
449C4×C139D4211yescharacteristic
450C4×C139D4211yescharacteristic
451C4×C139#54611yescharacteristic
452C4×C139#54611yescharacteristic
453C2×C139—42no—
454C2×C139—42no—
455C2×C139—42no—
456C2×C139—82no—
457C2×C139#241011yescharacteristic
458C2×C139#300511yescharacteristic
459C2×C139#300711yescharacteristic
460C2×C139#305411yescharacteristic
461C2×C139#305611yescharacteristic
462C2×C139#319611yescharacteristic
463C2×C139#319711yescharacteristic
464#24389C13911yesmaximal, characteristic, direct product factor, Sylow
465C139#2438911yescharacteristic, direct product factor, Sylow
466C2×#525C2×C13911yescharacteristic
467C2×#470C2×C13911yescharacteristic, complemented
468C2×#468C2×C13911yescharacteristic, complemented
469C2×#452C2×C13911yescharacteristic, complemented
470C2×#407C2×C13911yescharacteristic, complemented
471#2848C2×C13911yescharacteristic, complemented
472#2036C2×C13911yescharacteristic, complemented
473#2034C2×C13911yescharacteristic, complemented
474#2001C2×C13911yescharacteristic, complemented
475#2000C2×C13911yescharacteristic, complemented
476#1895C2×C13911yescharacteristic, complemented
477#1894C2×C13911yescharacteristic, complemented
478#1873C2×C13911yescharacteristic, complemented
479#1854C2×C13911yescharacteristic, complemented
480#1788C2×C13911yescharacteristic, complemented
481C22×#41C22×C13911yescharacteristic
482C24×C4C22×C13911yescharacteristic
483C22×Q16C22×C13911yescharacteristic, complemented
484C22×SD16C22×C13911yescharacteristic, complemented
485C22×M16C22×C13911yescharacteristic
486C22×M16C22×C13911yescharacteristic
487#525—24no—
488#525—24no—
489C2×#123—21no—
490C2×C22⋊Q8C22×C13911yescharacteristic
491C2×C22⋊Q8C22×C13911yescharacteristic
492C2×C22⋊Q8C22×C13911yescharacteristic
493C2×C22⋊Q8C22×C13911yescharacteristic
494C2×C22⋊Q8C22×C13911yescharacteristic
495C2×#121C22×C13911yescharacteristic
496C2×#121C22×C13911yescharacteristic
497C2×#120—21no—
498C2×C4×D4—21no—
499C2×C4×D4—21no—
500C2×#117C22×C13911yescharacteristic
501#470—24no—
502#468—24no—
503#452—24no—
504C2×#107C22×C13911yescharacteristic, complemented
505C2×#106C22×C13911yescharacteristic, complemented
506C2×#103C22×C13911yescharacteristic, complemented
507C2×#103C22×C13911yescharacteristic, complemented
508C2×#103C22×C13911yescharacteristic, complemented
509C2×#103C22×C13911yescharacteristic, complemented
510C2×#103C22×C13911yescharacteristic, complemented
511C2×#102C22×C13911yescharacteristic, complemented
512C2×#102C22×C13911yescharacteristic, complemented
513C2×#102C22×C13911yescharacteristic, complemented
514#407—24no—
515C2×C22⋊C8C22×C13911yescharacteristic
516C2×C22⋊C8C22×C13911yescharacteristic
517C2×C22⋊C8C22×C13911yescharacteristic
518C2×C22⋊C8C22×C13911yescharacteristic
519#385—21no—
520#385—21no—
521#385—21no—
522#380C22×C13911yescharacteristic
523#380C22×C13911yescharacteristic
524#380C22×C13911yescharacteristic
525#379—21no—
526#340C22×C13911yescharacteristic, complemented
527#340C22×C13911yescharacteristic, complemented
528#340C22×C13911yescharacteristic, complemented
529#340C22×C13911yescharacteristic, complemented
530C25D4×C13911yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C13911yescharacteristic
538C22×Q8C23×C13911yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C13911yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C13911yescharacteristic
551C23×C4D4×C13911yescharacteristic
552C23×C4D4×C13911yescharacteristic
553C23×C4C23×C13911yescharacteristic
554C23×C4C23×C13911yescharacteristic
555C23×C4C23×C13911yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C13911yescharacteristic
569C22×C8C23×C13911yescharacteristic
570C22×C8C23×C13911yescharacteristic
571C22×C8C23×C13911yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C13914yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C13914yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C13911yescharacteristic
598C2×C4⋊C4C23×C13911yescharacteristic
599C2×C4⋊C4C23×C13911yescharacteristic
600C2×C4⋊C4C23×C13911yescharacteristic
601C2×C4⋊C4C23×C13911yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C13914yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C13911yescharacteristic
640C24C2×D4×C13911yescharacteristic
641C24C2×D4×C13911yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C13912yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C13912yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C13911yescharacteristic
711C22×C4C2×D4×C13911yescharacteristic
712C22×C4C2×D4×C13912yes—
713C22×C4C2×D4×C13912yes—
714C22×C4C2×D4×C13911yescharacteristic
715C22×C4C2×D4×C13912yes—
716C22×C4#41×C13912yes—
717C22×C4C24×C13911yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C13912yes—
733C2×C8C2×D4×C13912yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C13912yes—
748C4⋊C4C2×D4×C13912yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C13912yes—
794C23#121×C13912yes—
795C23#137×C13912yes—
796C23C22×D4×C13911yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C13912yes—
857C2×C4#121×C13912yes—
858C2×C4C22×D4×C13911yescharacteristic
859C2×C4C22×D4×C13911yescharacteristic
860C2×C4C22×D4×C13911yescharacteristic
861C2×C4C2×#41×C13911yescharacteristic
862C2×C4H(5,𝔽2)×C13911yescharacteristic
863C2×C4H(5,𝔽2)×C13911yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C13911yescharacteristic
898C22C2×#121×C13911yescharacteristic
899C22#534×C13911yescharacteristic
900C22C2×#137×C13911yescharacteristic
901C22#575×C13911yescharacteristic
902C22#575×C13911yescharacteristic
903C22#575×C13911yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C13911yescharacteristic
915C4D42×C13911yescharacteristic
916C4#546×C13911yescharacteristic
917C4#546×C13911yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2#2410×C13911yescharacteristic
923C2#3005×C13911yescharacteristic
924C2#3007×C13911yescharacteristic
925C2#3054×C13911yescharacteristic
926C2#3056×C13911yescharacteristic
927C2#3196×C13911yescharacteristic
928C2#3197×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#525×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C139C2semidirect
3. C2×#468×C139C2semidirect
4. C2×#452×C139C2semidirect
5. C2×#407×C139C2semidirect
6. #2848×C139C2semidirect
7. #2036×C139C2semidirect
8. #2034×C139C2semidirect
9. #2001×C139C2semidirect
10. #2000×C139C2semidirect
11. #1895×C139C2semidirect
12. #1894×C139C2semidirect
13. #1873×C139C2semidirect
14. #1854×C139C2semidirect
15. #1788×C139C2semidirect
18. C22×Q16×C139C22semidirect
19. C22×SD16×C139C22semidirect
39. C2×#107×C139C22semidirect
40. C2×#106×C139C22semidirect
41. C2×#103×C139C22semidirect
42. C2×#103×C139C22semidirect
43. C2×#103×C139C22semidirect
44. C2×#103×C139C22semidirect
45. C2×#103×C139C22semidirect
46. C2×#102×C139C22semidirect
47. C2×#102×C139C22semidirect
48. C2×#102×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
162. C22⋊C8×C139D4semidirect
464. #24389C139direct (N × H)
465. C139#24389direct (N × H)
467. C2×#470C2×C139semidirect
468. C2×#468C2×C139semidirect
469. C2×#452C2×C139semidirect
470. C2×#407C2×C139semidirect
471. #2848C2×C139semidirect
472. #2036C2×C139semidirect
473. #2034C2×C139semidirect
474. #2001C2×C139semidirect
475. #2000C2×C139semidirect
476. #1895C2×C139semidirect
477. #1894C2×C139semidirect
478. #1873C2×C139semidirect
479. #1854C2×C139semidirect
480. #1788C2×C139semidirect
483. C22×Q16C22×C139semidirect
484. C22×SD16C22×C139semidirect
504. C2×#107C22×C139semidirect
505. C2×#106C22×C139semidirect
506. C2×#103C22×C139semidirect
507. C2×#103C22×C139semidirect
508. C2×#103C22×C139semidirect
509. C2×#103C22×C139semidirect
510. C2×#103C22×C139semidirect
511. C2×#102C22×C139semidirect
512. C2×#102C22×C139semidirect
513. C2×#102C22×C139semidirect
526. #340C22×C139semidirect
527. #340C22×C139semidirect
528. #340C22×C139semidirect
529. #340C22×C139semidirect
627. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1392
C2×#470×C1392
C2×#468×C1392
C2×#452×C1392
C2×#407×C1392
#2848×C1392
#2036×C1392
#2034×C1392
#2001×C1392
#2000×C1392
#1895×C1392
#1894×C1392
#1873×C1392
#1854×C1392
#1788×C1392
#24389139