Finite Group Databasebeta

← C139×#24396 #48018992

Subgroups — C139×#24396 #48018992

Order 35584.

1444 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C139C211yesmaximal, characteristic, complemented
2C2×#468×C139C211yesmaximal, characteristic, complemented
3C2×#465×C139C211yesmaximal, characteristic, complemented
4C2×#448×C139C211yesmaximal, characteristic, complemented
5C2×#408×C139C211yesmaximal, characteristic, complemented
6#2615×C139C211yesmaximal, characteristic
7#2036×C139C211yesmaximal, characteristic, complemented
8#2035×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1894×C139C211yesmaximal, characteristic, complemented
12#1892×C139C211yesmaximal, characteristic, complemented
13#1875×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1787×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic
21C23×C8×C139C2211yescharacteristic
22#536×C139—24no—
23#536×C139—24no—
24C2×C4⋊Q8×C139—21no—
25C2×#124×C139—21no—
26C2×#123×C139—21no—
27C2×#123×C139—21no—
28C2×C22⋊Q8×C139C2211yescharacteristic
29C2×C22⋊Q8×C139C2211yescharacteristic
30C2×C22⋊Q8×C139C2211yescharacteristic
31C2×C22⋊Q8×C139C2211yescharacteristic
32C2×#121×C139C2211yescharacteristic
33C2×#121×C139C2211yescharacteristic
34C2×#121×C139C2211yescharacteristic
35C2×#117×C139C2211yescharacteristic
36#468×C139—24no—
37#465×C139—24no—
38#448×C139—24no—
39C2×#107×C139C2211yescharacteristic
40C2×#106×C139C2211yescharacteristic
41C2×#103×C139C2211yescharacteristic
42C2×#103×C139C2211yescharacteristic
43C2×#103×C139C2211yescharacteristic
44C2×#103×C139C2211yescharacteristic
45C2×#103×C139C2211yescharacteristic
46C2×#103×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49#408×C139—24no—
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54#393×C139—21no—
55#392×C139—21no—
56#392×C139—21no—
57#392×C139—21no—
58#380×C139C2211yescharacteristic
59#380×C139C2211yescharacteristic
60#380×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63#340×C139C2211yescharacteristic
64#340×C139C2211yescharacteristic
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—41no—
70C2×#41×C139—41no—
71C22×Q8×C139—22no—
72C22×Q8×C139—22no—
73C22×Q8×C139—21no—
74C22×Q8×C139—22no—
75C22×Q8×C139—22no—
76C22×Q8×C139—41no—
77C22×Q8×C139—41no—
78C22×Q8×C139D411yescharacteristic
79C22×Q8×C139C2311yescharacteristic
80C22×Q8×C139C2311yescharacteristic
81C22×D4×C139—21no—
82C22×D4×C139—21no—
83C22×D4×C139—21no—
84C22×D4×C139D411yescharacteristic
85C22×D4×C139D411yescharacteristic
86C22×D4×C139D411yescharacteristic
87C22×D4×C139C2311yescharacteristic
88C23×C4×C139—21no—
89C23×C4×C139C2311yescharacteristic
90C23×C4×C139C2311yescharacteristic
91C23×C4×C139C2311yescharacteristic
92C2×SD16×C139—22no—
93C2×SD16×C139—22no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—41no—
97C2×SD16×C139—41no—
98C2×M16×C139—22no—
99C2×M16×C139—22no—
100C2×M16×C139—41no—
101C22×C8×C139—22no—
102C22×C8×C139—22no—
103C22×C8×C139—41no—
104C22×C8×C139C2311yescharacteristic
105C22×C8×C139C2311yescharacteristic
106C22×C8×C139C2311yescharacteristic
107C22×C8×C139C2311yescharacteristic
108C4⋊Q8×C139—28no—
109#124×C139—28no—
110#123×C139—28no—
111#123×C139—28no—
112C22⋊Q8×C139—22no—
113C22⋊Q8×C139—22no—
114C22⋊Q8×C139—22no—
115C22⋊Q8×C139—22no—
116C22⋊Q8×C139—22no—
117C22⋊Q8×C139—22no—
118C22⋊Q8×C139D414yescomplemented
119C22⋊Q8×C139D414yescomplemented
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139—22no—
124#121×C139—41no—
125#121×C139—41no—
126#117×C139—22no—
127#117×C139—22no—
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#103×C139—41no—
157#102×C139—22no—
158#102×C139—22no—
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—21no—
167C24×C139C2×D411yescharacteristic
168C24×C139C2×D411yescharacteristic
169C24×C139C2×D411yescharacteristic
170#41×C139—44no—
171#41×C139—44no—
172#41×C139—44no—
173#41×C139—44no—
174C2×Q8×C139—24no—
175C2×Q8×C139—22no—
176C2×Q8×C139—22no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
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—41no—
188C2×Q8×C139—44no—
189C2×Q8×C139—44no—
190C2×Q8×C139—44no—
191C2×Q8×C139—44no—
192C2×Q8×C139—42no—
193C2×Q8×C139—42no—
194C2×Q8×C139C2×D412yes—
195C2×Q8×C139C2×D412yes—
196C2×D4×C139—22no—
197C2×D4×C139—22no—
198C2×D4×C139—22no—
199C2×D4×C139—22no—
200C2×D4×C139—22no—
201C2×D4×C139—22no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—41no—
209C2×D4×C139—41no—
210C2×D4×C139—41no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—81no—
215C2×D4×C139—81no—
216C2×D4×C139—81no—
217C2×D4×C139—81no—
218C2×D4×C139—81no—
219C2×D4×C139—81no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—24no—
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—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—42no—
243C22×C4×C139—42no—
244C22×C4×C139C2×D411yescharacteristic
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D412yes—
247C22×C4×C139C2×D412yes—
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2×D412yes—
250C22×C4×C139#4112yes—
251C22×C4×C139C2411yescharacteristic
252SD16×C139—44no—
253SD16×C139—44no—
254M16×C139—44no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
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—44no—
266C2×C8×C139C2×D412yes—
267C2×C8×C139C2×D412yes—
268C4⋊C4×C139—24no—
269C4⋊C4×C139—24no—
270C4⋊C4×C139—24no—
271C4⋊C4×C139—24no—
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—21no—
280C4⋊C4×C139C2×D412yes—
281C4⋊C4×C139C2×D412yes—
282C22⋊C4×C139—24no—
283C22⋊C4×C139—24no—
284C22⋊C4×C139—24no—
285C22⋊C4×C139—24no—
286C22⋊C4×C139—24no—
287C22⋊C4×C139—42no—
288C22⋊C4×C139—42no—
289C22⋊C4×C139—42no—
290C22⋊C4×C139—81no—
291C22⋊C4×C139—81no—
292C22⋊C4×C139—81no—
293C42×C139—24no—
294C23×C139—21no—
295C23×C139—21no—
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—41no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139#12012yes—
321C23×C139#12112yes—
322C23×C139C22×D411yescharacteristic
323Q8×C139—22no—
324Q8×C139—22no—
325Q8×C139—22no—
326Q8×C139—22no—
327Q8×C139—44no—
328Q8×C139—48no—
329Q8×C139—41no—
330Q8×C139—41no—
331Q8×C139—41no—
332Q8×C139—41no—
333D4×C139—44no—
334D4×C139—44no—
335D4×C139—44no—
336D4×C139—41no—
337D4×C139—41no—
338D4×C139—41no—
339D4×C139—41no—
340D4×C139—84no—
341D4×C139—84no—
342D4×C139—84no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—22no—
348C2×C4×C139—22no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
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—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—48no—
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—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#12012yes—
385C2×C4×C139#12112yes—
386C2×C4×C139C22×D411yescharacteristic
387C2×C4×C139C22×D411yescharacteristic
388C2×C4×C139C22×D411yescharacteristic
389C2×C4×C139C2×#4111yescharacteristic
390C2×C4×C139H(5,𝔽2)11yescharacteristic
391C2×C4×C139H(5,𝔽2)11yescharacteristic
392C8×C139—22no—
393C8×C139—22no—
394C8×C139—41no—
395C8×C139—41no—
396C22×C139—22no—
397C22×C139—22no—
398C22×C139—22no—
399C22×C139—22no—
400C22×C139—22no—
401C22×C139—22no—
402C22×C139—41no—
403C22×C139—41no—
404C22×C139—41no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—41no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—41no—
414C22×C139—41no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—81no—
418C22×C139—81no—
419C22×C139—81no—
420C22×C139—81no—
421C22×C139—81no—
422C22×C139—81no—
423C22×C139—81no—
424C22×C139C2×#12011yescharacteristic
425C22×C139C2×#12111yescharacteristic
426C22×C139#53411yescharacteristic
427C22×C139#57711yescharacteristic
428C22×C139#57711yescharacteristic
429C22×C139#57711yescharacteristic
430C22×C139#57811yescharacteristic
431C4×C139—22no—
432C4×C139—22no—
433C4×C139—41no—
434C4×C139—42no—
435C4×C139—42no—
436C4×C139—42no—
437C4×C139—42no—
438C4×C139—81no—
439C4×C139—81no—
440C4×C139—81no—
441C4×C139D4211yescharacteristic
442C4×C139D4211yescharacteristic
443C4×C139#54611yescharacteristic
444C4×C139#54611yescharacteristic
445C2×C139—42no—
446C2×C139—42no—
447C2×C139—81no—
448C2×C139—161no—
449C2×C139#241011yescharacteristic
450C2×C139#301011yescharacteristic
451C2×C139#301311yescharacteristic
452C2×C139#305711yescharacteristic
453C2×C139#306311yescharacteristic
454C2×C139#320011yescharacteristic
455C2×C139#320111yescharacteristic
456#24396C13911yesmaximal, characteristic, direct product factor, Sylow
457C139#2439611yescharacteristic, direct product factor, Sylow
458C2×#536C2×C13911yescharacteristic, complemented
459C2×#468C2×C13911yescharacteristic, complemented
460C2×#465C2×C13911yescharacteristic, complemented
461C2×#448C2×C13911yescharacteristic, complemented
462C2×#408C2×C13911yescharacteristic, complemented
463#2615C2×C13911yescharacteristic
464#2036C2×C13911yescharacteristic, complemented
465#2035C2×C13911yescharacteristic, complemented
466#2000C2×C13911yescharacteristic, complemented
467#2000C2×C13911yescharacteristic, complemented
468#1894C2×C13911yescharacteristic, complemented
469#1892C2×C13911yescharacteristic, complemented
470#1875C2×C13911yescharacteristic, complemented
471#1854C2×C13911yescharacteristic, complemented
472#1787C2×C13911yescharacteristic, complemented
473C22×#41C22×C13911yescharacteristic
474C23×Q8C22×C13911yescharacteristic
475C22×SD16C22×C13911yescharacteristic
476C22×SD16C22×C13911yescharacteristic
477C22×M16C22×C13911yescharacteristic
478C23×C8C22×C13911yescharacteristic
479#536—24no—
480#536—24no—
481C2×C4⋊Q8—21no—
482C2×#124—21no—
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C22×C13911yescharacteristic
486C2×C22⋊Q8C22×C13911yescharacteristic
487C2×C22⋊Q8C22×C13911yescharacteristic
488C2×C22⋊Q8C22×C13911yescharacteristic
489C2×#121C22×C13911yescharacteristic
490C2×#121C22×C13911yescharacteristic
491C2×#121C22×C13911yescharacteristic
492C2×#117C22×C13911yescharacteristic
493#468—24no—
494#465—24no—
495#448—24no—
496C2×#107C22×C13911yescharacteristic
497C2×#106C22×C13911yescharacteristic
498C2×#103C22×C13911yescharacteristic
499C2×#103C22×C13911yescharacteristic
500C2×#103C22×C13911yescharacteristic
501C2×#103C22×C13911yescharacteristic
502C2×#103C22×C13911yescharacteristic
503C2×#103C22×C13911yescharacteristic
504C2×#102C22×C13911yescharacteristic
505C2×#102C22×C13911yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C13911yescharacteristic
508C2×C22⋊C8C22×C13911yescharacteristic
509C2×C22⋊C8C22×C13911yescharacteristic
510C2×C22⋊C8C22×C13911yescharacteristic
511#393—21no—
512#392—21no—
513#392—21no—
514#392—21no—
515#380C22×C13911yescharacteristic
516#380C22×C13911yescharacteristic
517#380C22×C13911yescharacteristic
518#340C22×C13911yescharacteristic
519#340C22×C13911yescharacteristic
520#340C22×C13911yescharacteristic
521#340C22×C13911yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8D4×C13911yescharacteristic
536C22×Q8C23×C13911yescharacteristic
537C22×Q8C23×C13911yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C13911yescharacteristic
542C22×D4D4×C13911yescharacteristic
543C22×D4D4×C13911yescharacteristic
544C22×D4C23×C13911yescharacteristic
545C23×C4—21no—
546C23×C4C23×C13911yescharacteristic
547C23×C4C23×C13911yescharacteristic
548C23×C4C23×C13911yescharacteristic
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C13911yescharacteristic
562C22×C8C23×C13911yescharacteristic
563C22×C8C23×C13911yescharacteristic
564C22×C8C23×C13911yescharacteristic
565C4⋊Q8—28no—
566#124—28no—
567#123—28no—
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8D4×C13914yescomplemented
576C22⋊Q8D4×C13914yescomplemented
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#117—22no—
584#117—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4C23×C13911yescharacteristic
590C2×C4⋊C4C23×C13911yescharacteristic
591C2×C4⋊C4C23×C13911yescharacteristic
592C2×C4⋊C4C23×C13911yescharacteristic
593C2×C4⋊C4C23×C13911yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C42—21no—
606#107—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#103—41no—
614#102—22no—
615#102—22no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C13914yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C13911yescharacteristic
625C24C2×D4×C13911yescharacteristic
626C24C2×D4×C13911yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631C2×Q8—24no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—41no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8C2×D4×C13912yes—
652C2×Q8C2×D4×C13912yes—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
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—42no—
700C22×C4—42no—
701C22×C4C2×D4×C13911yescharacteristic
702C22×C4C2×D4×C13911yescharacteristic
703C22×C4C2×D4×C13912yes—
704C22×C4C2×D4×C13912yes—
705C22×C4C2×D4×C13911yescharacteristic
706C22×C4C2×D4×C13912yes—
707C22×C4#41×C13912yes—
708C22×C4C24×C13911yescharacteristic
709SD16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C13912yes—
724C2×C8C2×D4×C13912yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4C2×D4×C13912yes—
738C4⋊C4C2×D4×C13912yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—81no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C42—24no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C13912yes—
778C23#121×C13912yes—
779C23C22×D4×C13911yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—48no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
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—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C13912yes—
842C2×C4#121×C13912yes—
843C2×C4C22×D4×C13911yescharacteristic
844C2×C4C22×D4×C13911yescharacteristic
845C2×C4C22×D4×C13911yescharacteristic
846C2×C4C2×#41×C13911yescharacteristic
847C2×C4H(5,𝔽2)×C13911yescharacteristic
848C2×C4H(5,𝔽2)×C13911yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C13911yescharacteristic
882C22C2×#121×C13911yescharacteristic
883C22#534×C13911yescharacteristic
884C22#577×C13911yescharacteristic
885C22#577×C13911yescharacteristic
886C22#577×C13911yescharacteristic
887C22#578×C13911yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C13911yescharacteristic
899C4D42×C13911yescharacteristic
900C4#546×C13911yescharacteristic
901C4#546×C13911yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—161no—
906C2#2410×C13911yescharacteristic
907C2#3010×C13911yescharacteristic
908C2#3013×C13911yescharacteristic
909C2#3057×C13911yescharacteristic
910C2#3063×C13911yescharacteristic
911C2#3200×C13911yescharacteristic
912C2#3201×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2615×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#536×C139C2semidirect
2. C2×#468×C139C2semidirect
3. C2×#465×C139C2semidirect
4. C2×#448×C139C2semidirect
5. C2×#408×C139C2semidirect
7. #2036×C139C2semidirect
8. #2035×C139C2semidirect
9. #2000×C139C2semidirect
10. #2000×C139C2semidirect
11. #1894×C139C2semidirect
12. #1892×C139C2semidirect
13. #1875×C139C2semidirect
14. #1854×C139C2semidirect
15. #1787×C139C2semidirect
118. C22⋊Q8×C139D4semidirect
119. C22⋊Q8×C139D4semidirect
162. C22⋊C8×C139D4semidirect
456. #24396C139direct (N × H)
457. C139#24396direct (N × H)
458. C2×#536C2×C139semidirect
459. C2×#468C2×C139semidirect
460. C2×#465C2×C139semidirect
461. C2×#448C2×C139semidirect
462. C2×#408C2×C139semidirect
464. #2036C2×C139semidirect
465. #2035C2×C139semidirect
466. #2000C2×C139semidirect
467. #2000C2×C139semidirect
468. #1894C2×C139semidirect
469. #1892C2×C139semidirect
470. #1875C2×C139semidirect
471. #1854C2×C139semidirect
472. #1787C2×C139semidirect
575. C22⋊Q8D4×C139semidirect
576. C22⋊Q8D4×C139semidirect
619. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1392
C2×#468×C1392
C2×#465×C1392
C2×#448×C1392
C2×#408×C1392
#2615×C1392
#2036×C1392
#2035×C1392
#2000×C1392
#1894×C1392
#1892×C1392
#1875×C1392
#1854×C1392
#1787×C1392
#24396139