Finite Group Databasebeta

← C139×#25390 #48019986

Subgroups — C139×#25390 #48019986

Order 35584.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#468×C139C211yesmaximal, characteristic, complemented
3C2×#463×C139C211yesmaximal, characteristic, complemented
4C2×#436×C139C211yesmaximal, characteristic, complemented
5#2540×C139C211yesmaximal, characteristic, complemented
6#2535×C139C211yesmaximal, characteristic, complemented
7#2035×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1958×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1894×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20C2×#124×C139C2211yescharacteristic
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29#469×C139—24no—
30#468×C139—24no—
31#463×C139—24no—
32#436×C139—24no—
33C2×#107×C139C2211yescharacteristic
34C2×#106×C139C2211yescharacteristic
35C2×C4⋊C8×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C4×C8×C139C2211yescharacteristic
47#399×C139—21no—
48#397×C139—21no—
49#392×C139—21no—
50#392×C139—21no—
51#390×C139—21no—
52#390×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#382×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58C4×C4⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139D411yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139C2311yescharacteristic
73C23×C4×C139C2311yescharacteristic
74C2×SD16×C139—22no—
75C2×SD16×C139—22no—
76C2×SD16×C139—41no—
77C2×D8×C139—22no—
78C2×D8×C139—22no—
79C2×D8×C139—41no—
80C2×M16×C139—22no—
81C2×M16×C139—22no—
82C2×M16×C139—22no—
83C2×M16×C139—22no—
84C2×M16×C139—41no—
85C2×M16×C139—41no—
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90#124×C139—22no—
91#124×C139—22no—
92C22⋊Q8×C139—22no—
93C22⋊Q8×C139—22no—
94C22⋊Q8×C139—41no—
95C22⋊Q8×C139—41no—
96#121×C139—22no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—41no—
101#121×C139—41no—
102#121×C139—41no—
103#121×C139—41no—
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139D411yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C42×C139—21no—
130C2×C42×C139C2311yescharacteristic
131#107×C139—22no—
132#106×C139—22no—
133C4⋊C8×C139D414yescomplemented
134#103×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—41no—
141#102×C139D414yescomplemented
142C22⋊C8×C139—22no—
143C22⋊C8×C139—22no—
144C4×C8×C139—22no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150C24×C139—21no—
151C24×C139—21no—
152C24×C139C2×D411yescharacteristic
153C24×C139C2×D411yescharacteristic
154C2×Q8×C139—21no—
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—21no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×D4×C139—22no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—41no—
173C2×D4×C139—41no—
174C2×D4×C139—42no—
175C2×D4×C139—42no—
176C2×D4×C139—42no—
177C2×D4×C139—42no—
178C2×D4×C139—42no—
179C2×D4×C139—42no—
180C2×D4×C139—42no—
181C2×D4×C139—42no—
182C2×D4×C139—81no—
183C2×D4×C139—81no—
184C2×D4×C139—81no—
185C2×D4×C139—81no—
186C2×D4×C139C2×D412yes—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
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—42no—
206C22×C4×C139—81no—
207C22×C4×C139—81no—
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2411yescharacteristic
213SD16×C139—44no—
214D8×C139—44no—
215M16×C139—44no—
216M16×C139—44no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139—21no—
220C2×C8×C139—21no—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139C2×D412yes—
227C2×C8×C139C2×D412yes—
228C2×C8×C139C2×D412yes—
229C4⋊C4×C139—22no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—42no—
239C4⋊C4×C139—42no—
240C4⋊C4×C139C2×D412yes—
241C4⋊C4×C139#4112yes—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—22no—
244C22⋊C4×C139—42no—
245C22⋊C4×C139—42no—
246C22⋊C4×C139—42no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—81no—
254C22⋊C4×C139—81no—
255C42×C139—81no—
256C42×C139C2×D412yes—
257C42×C139#4112yes—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—22no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139C22×D411yescharacteristic
287Q8×C139—41no—
288Q8×C139—41no—
289Q8×C139—41no—
290Q8×C139—41no—
291D4×C139—22no—
292D4×C139—22no—
293D4×C139—44no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—84no—
301D4×C139—84no—
302D4×C139—84no—
303D4×C139—84no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—22no—
312C2×C4×C139—21no—
313C2×C4×C139—22no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—84no—
341C2×C4×C139#12112yes—
342C2×C4×C139#12112yes—
343C2×C4×C139C22×D411yescharacteristic
344C2×C4×C139C22×D411yescharacteristic
345C2×C4×C139C2×#4111yescharacteristic
346C2×C4×C139C2×#4111yescharacteristic
347C2×C4×C139H(5,𝔽2)11yescharacteristic
348C2×C4×C139H(5,𝔽2)11yescharacteristic
349C8×C139—22no—
350C8×C139—22no—
351C8×C139—22no—
352C8×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—42no—
356C22×C139—41no—
357C22×C139—41no—
358C22×C139—42no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—41no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139C2×#12111yescharacteristic
382C22×C139D4211yescharacteristic
383C22×C139#54611yescharacteristic
384C22×C139#57511yescharacteristic
385C22×C139#57511yescharacteristic
386C22×C139#57611yescharacteristic
387C22×C139#57711yescharacteristic
388C4×C139—22no—
389C4×C139—22no—
390C4×C139—41no—
391C4×C139—41no—
392C4×C139—42no—
393C4×C139—42no—
394C4×C139—81no—
395C4×C139—81no—
396C4×C139—81no—
397C4×C139—81no—
398C4×C139#53211yescharacteristic
399C4×C139#54011yescharacteristic
400C4×C139D4211yescharacteristic
401C4×C139#55011yescharacteristic
402C2×C139—81no—
403C2×C139—81no—
404C2×C139—82no—
405C2×C139—161no—
406C2×C139#242811yescharacteristic
407C2×C139#305411yescharacteristic
408C2×C139#306211yescharacteristic
409C2×C139#327311yescharacteristic
410C2×C139#327511yescharacteristic
411C2×C139#332211yescharacteristic
412C2×C139#332611yescharacteristic
413#25390C13911yesmaximal, characteristic, direct product factor, Sylow
414C139#2539011yescharacteristic, direct product factor, Sylow
415C2×#469C2×C13911yescharacteristic, complemented
416C2×#468C2×C13911yescharacteristic, complemented
417C2×#463C2×C13911yescharacteristic, complemented
418C2×#436C2×C13911yescharacteristic, complemented
419#2540C2×C13911yescharacteristic, complemented
420#2535C2×C13911yescharacteristic, complemented
421#2035C2×C13911yescharacteristic, complemented
422#2033C2×C13911yescharacteristic, complemented
423#2000C2×C13911yescharacteristic, complemented
424#1999C2×C13911yescharacteristic, complemented
425#1958C2×C13911yescharacteristic, complemented
426#1949C2×C13911yescharacteristic, complemented
427#1895C2×C13911yescharacteristic, complemented
428#1894C2×C13911yescharacteristic, complemented
429C4×#102C2×C13911yescharacteristic, complemented
430C22×SD16C22×C13911yescharacteristic
431C22×D8C22×C13911yescharacteristic
432C22×M16C22×C13911yescharacteristic
433C22×M16C22×C13911yescharacteristic
434C2×#124C22×C13911yescharacteristic
435C2×C22⋊Q8C22×C13911yescharacteristic
436C2×C22⋊Q8C22×C13911yescharacteristic
437C2×#121C22×C13911yescharacteristic
438C2×#121C22×C13911yescharacteristic
439C2×#121C22×C13911yescharacteristic
440C2×#121C22×C13911yescharacteristic
441C2×C4×D4C22×C13911yescharacteristic
442C2×C4×D4C22×C13911yescharacteristic
443#469—24no—
444#468—24no—
445#463—24no—
446#436—24no—
447C2×#107C22×C13911yescharacteristic
448C2×#106C22×C13911yescharacteristic
449C2×C4⋊C8C22×C13911yescharacteristic
450C2×#103C22×C13911yescharacteristic
451C2×#103C22×C13911yescharacteristic
452C2×#103C22×C13911yescharacteristic
453C2×#102C22×C13911yescharacteristic
454C2×#102C22×C13911yescharacteristic
455C2×#102C22×C13911yescharacteristic
456C2×#102C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×C22⋊C8C22×C13911yescharacteristic
459C2×C22⋊C8C22×C13911yescharacteristic
460C2×C4×C8C22×C13911yescharacteristic
461#399—21no—
462#397—21no—
463#392—21no—
464#392—21no—
465#390—21no—
466#390—21no—
467#386—21no—
468#386—21no—
469#382C22×C13911yescharacteristic
470#380C22×C13911yescharacteristic
471#380C22×C13911yescharacteristic
472C4×C4⋊C4C22×C13911yescharacteristic
473#340C22×C13911yescharacteristic
474#340C22×C13911yescharacteristic
475#340C22×C13911yescharacteristic
476#340C22×C13911yescharacteristic
477C22×Q8C23×C13911yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C13911yescharacteristic
483C22×D4C23×C13911yescharacteristic
484C22×D4C23×C13911yescharacteristic
485C23×C4—21no—
486C23×C4C23×C13911yescharacteristic
487C23×C4C23×C13911yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C22×C8C23×C13911yescharacteristic
501C22×C8C23×C13911yescharacteristic
502C22×C8C23×C13911yescharacteristic
503C22×C8C23×C13911yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C13911yescharacteristic
525C2×C4⋊C4C23×C13911yescharacteristic
526C2×C4⋊C4C23×C13911yescharacteristic
527C2×C4⋊C4C23×C13911yescharacteristic
528C2×C4⋊C4C23×C13911yescharacteristic
529C2×C4⋊C4C23×C13911yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C13911yescharacteristic
542C2×C22⋊C4D4×C13911yescharacteristic
543C2×C42—21no—
544C2×C42C23×C13911yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C13914yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C13914yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C13911yescharacteristic
567C24C2×D4×C13911yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C13912yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C13911yescharacteristic
623C22×C4C2×D4×C13911yescharacteristic
624C22×C4C2×D4×C13911yescharacteristic
625C22×C4C2×D4×C13911yescharacteristic
626C22×C4C24×C13911yescharacteristic
627SD16—44no—
628D8—44no—
629M16—44no—
630M16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C2×D4×C13912yes—
641C2×C8C2×D4×C13912yes—
642C2×C8C2×D4×C13912yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C13912yes—
655C4⋊C4#41×C13912yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C13912yes—
671C42#41×C13912yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23C22×D4×C13911yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—84no—
755C2×C4#121×C13912yes—
756C2×C4#121×C13912yes—
757C2×C4C22×D4×C13911yescharacteristic
758C2×C4C22×D4×C13911yescharacteristic
759C2×C4C2×#41×C13911yescharacteristic
760C2×C4C2×#41×C13911yescharacteristic
761C2×C4H(5,𝔽2)×C13911yescharacteristic
762C2×C4H(5,𝔽2)×C13911yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C13911yescharacteristic
796C22D42×C13911yescharacteristic
797C22#546×C13911yescharacteristic
798C22#575×C13911yescharacteristic
799C22#575×C13911yescharacteristic
800C22#576×C13911yescharacteristic
801C22#577×C13911yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4#532×C13911yescharacteristic
813C4#540×C13911yescharacteristic
814C4D42×C13911yescharacteristic
815C4#550×C13911yescharacteristic
816C2—81no—
817C2—81no—
818C2—82no—
819C2—161no—
820C2#2428×C13911yescharacteristic
821C2#3054×C13911yescharacteristic
822C2#3062×C13911yescharacteristic
823C2#3273×C13911yescharacteristic
824C2#3275×C13911yescharacteristic
825C2#3322×C13911yescharacteristic
826C2#3326×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
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×#469×C139C2semidirect
2. C2×#468×C139C2semidirect
3. C2×#463×C139C2semidirect
4. C2×#436×C139C2semidirect
5. #2540×C139C2semidirect
6. #2535×C139C2semidirect
7. #2035×C139C2semidirect
8. #2033×C139C2semidirect
9. #2000×C139C2semidirect
10. #1999×C139C2semidirect
11. #1958×C139C2semidirect
12. #1949×C139C2semidirect
13. #1895×C139C2semidirect
14. #1894×C139C2semidirect
15. C4×#102×C139C2semidirect
133. C4⋊C8×C139D4semidirect
141. #102×C139D4semidirect
413. #25390C139direct (N × H)
414. C139#25390direct (N × H)
415. C2×#469C2×C139semidirect
416. C2×#468C2×C139semidirect
417. C2×#463C2×C139semidirect
418. C2×#436C2×C139semidirect
419. #2540C2×C139semidirect
420. #2535C2×C139semidirect
421. #2035C2×C139semidirect
422. #2033C2×C139semidirect
423. #2000C2×C139semidirect
424. #1999C2×C139semidirect
425. #1958C2×C139semidirect
426. #1949C2×C139semidirect
427. #1895C2×C139semidirect
428. #1894C2×C139semidirect
429. C4×#102C2×C139semidirect
547. C4⋊C8D4×C139semidirect
555. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1392
C2×#468×C1392
C2×#463×C1392
C2×#436×C1392
#2540×C1392
#2535×C1392
#2035×C1392
#2033×C1392
#2000×C1392
#1999×C1392
#1958×C1392
#1949×C1392
#1895×C1392
#1894×C1392
C4×#102×C1392
#25390139