Finite Group Databasebeta

← C139×#25401 #48019997

Subgroups — C139×#25401 #48019997

Order 35584.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#465×C139C211yesmaximal, characteristic, complemented
3C2×#463×C139C211yesmaximal, characteristic, complemented
4C2×#435×C139C211yesmaximal, characteristic, complemented
5#2540×C139C211yesmaximal, characteristic, complemented
6#2537×C139C211yesmaximal, characteristic, complemented
7#2035×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1959×C139C211yesmaximal, characteristic, complemented
12#1948×C139C211yesmaximal, characteristic, complemented
13#1894×C139C211yesmaximal, characteristic, complemented
14#1893×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20C2×#124×C139C2211yescharacteristic
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×#121×C139—21no—
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30#469×C139—24no—
31#465×C139—24no—
32#463×C139—24no—
33#435×C139—24no—
34C2×#106×C139C2211yescharacteristic
35C2×#106×C139C2211yescharacteristic
36C2×C4⋊C8×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×#97×C139C2211yescharacteristic
48#399×C139—21no—
49#394×C139—21no—
50#394×C139—21no—
51#392×C139—21no—
52#390×C139—21no—
53#390×C139—21no—
54#384×C139C2211yescharacteristic
55#380×C139—21no—
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—41no—
83C22×C8×C139—22no—
84C22×C8×C139—22no—
85C22×C8×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—
104#121×C139—44no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108C4×D4×C139—22no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
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×C139—21no—
130C2×C22⋊C4×C139D411yescharacteristic
131C2×C22⋊C4×C139D411yescharacteristic
132C2×C42×C139—21no—
133C2×C42×C139C2311yescharacteristic
134#106×C139—22no—
135#106×C139—22no—
136C4⋊C8×C139D414yescomplemented
137#103×C139—22no—
138#103×C139—22no—
139#103×C139—41no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144#102×C139D414yescomplemented
145C22⋊C8×C139—22no—
146C22⋊C8×C139—22no—
147#97×C139—22no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139C2×D411yescharacteristic
154C24×C139C2×D411yescharacteristic
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—21no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×D4×C139—22no—
162C2×D4×C139—22no—
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—21no—
173C2×D4×C139—21no—
174C2×D4×C139—41no—
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—42no—
183C2×D4×C139—81no—
184C2×D4×C139—81no—
185C2×D4×C139—81no—
186C2×D4×C139—81no—
187C2×D4×C139C2×D412yes—
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—21no—
206C22×C4×C139—42no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2411yescharacteristic
214SD16×C139—44no—
215D8×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×C139—44no—
227C2×C8×C139C2×D412yes—
228C2×C8×C139C2×D412yes—
229C2×C8×C139C2×D412yes—
230C4⋊C4×C139—22no—
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—21no—
239C4⋊C4×C139—42no—
240C4⋊C4×C139—42no—
241C4⋊C4×C139—42no—
242C4⋊C4×C139—81no—
243C4⋊C4×C139C2×D412yes—
244C4⋊C4×C139#4112yes—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—22no—
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—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C42×C139—81no—
259C42×C139C2×D412yes—
260C42×C139#4112yes—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—22no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
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×C139—41no—
287C23×C139—41no—
288C23×C139AGL(1,ℤ/8)12yes—
289C23×C139C22×D411yescharacteristic
290Q8×C139—41no—
291Q8×C139—41no—
292Q8×C139—41no—
293Q8×C139—41no—
294D4×C139—22no—
295D4×C139—22no—
296D4×C139—44no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—84no—
304D4×C139—84no—
305D4×C139—84no—
306D4×C139—84no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
314C2×C4×C139—22no—
315C2×C4×C139—21no—
316C2×C4×C139—22no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
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—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—84no—
344C2×C4×C139#12112yes—
345C2×C4×C139#12112yes—
346C2×C4×C139C22×D411yescharacteristic
347C2×C4×C139C22×D411yescharacteristic
348C2×C4×C139C2×#4111yescharacteristic
349C2×C4×C139C2×#4111yescharacteristic
350C2×C4×C139H(5,𝔽2)11yescharacteristic
351C2×C4×C139H(5,𝔽2)11yescharacteristic
352C8×C139—22no—
353C8×C139—22no—
354C8×C139—22no—
355C8×C139—41no—
356C22×C139—22no—
357C22×C139—22no—
358C22×C139—22no—
359C22×C139—41no—
360C22×C139—41no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—42no—
365C22×C139—41no—
366C22×C139—42no—
367C22×C139—41no—
368C22×C139—42no—
369C22×C139—41no—
370C22×C139—41no—
371C22×C139—41no—
372C22×C139—41no—
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×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139C2×#12111yescharacteristic
385C22×C139D4211yescharacteristic
386C22×C139#54611yescharacteristic
387C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C139#57511yescharacteristic
389C22×C139#57711yescharacteristic
390C22×C139#57711yescharacteristic
391C4×C139—22no—
392C4×C139—22no—
393C4×C139—41no—
394C4×C139—41no—
395C4×C139—42no—
396C4×C139—42no—
397C4×C139—81no—
398C4×C139—81no—
399C4×C139—81no—
400C4×C139—81no—
401C4×C139#53211yescharacteristic
402C4×C139#54011yescharacteristic
403C4×C139D4211yescharacteristic
404C4×C139#55011yescharacteristic
405C2×C139—42no—
406C2×C139—81no—
407C2×C139—82no—
408C2×C139—161no—
409C2×C139#242811yescharacteristic
410C2×C139#305511yescharacteristic
411C2×C139#306011yescharacteristic
412C2×C139#326511yescharacteristic
413C2×C139#326711yescharacteristic
414C2×C139#330611yescharacteristic
415C2×C139#332111yescharacteristic
416#25401C13911yesmaximal, characteristic, direct product factor, Sylow
417C139#2540111yescharacteristic, direct product factor, Sylow
418C2×#469C2×C13911yescharacteristic, complemented
419C2×#465C2×C13911yescharacteristic, complemented
420C2×#463C2×C13911yescharacteristic, complemented
421C2×#435C2×C13911yescharacteristic, complemented
422#2540C2×C13911yescharacteristic, complemented
423#2537C2×C13911yescharacteristic, complemented
424#2035C2×C13911yescharacteristic, complemented
425#2034C2×C13911yescharacteristic, complemented
426#2000C2×C13911yescharacteristic, complemented
427#1999C2×C13911yescharacteristic, complemented
428#1959C2×C13911yescharacteristic, complemented
429#1948C2×C13911yescharacteristic, complemented
430#1894C2×C13911yescharacteristic, complemented
431#1893C2×C13911yescharacteristic, complemented
432#1762C2×C13911yescharacteristic, complemented
433C22×SD16C22×C13911yescharacteristic
434C22×D8C22×C13911yescharacteristic
435C22×M16C22×C13911yescharacteristic
436C23×C8C22×C13911yescharacteristic
437C2×#124C22×C13911yescharacteristic
438C2×C22⋊Q8C22×C13911yescharacteristic
439C2×C22⋊Q8C22×C13911yescharacteristic
440C2×#121—21no—
441C2×#121C22×C13911yescharacteristic
442C2×#121C22×C13911yescharacteristic
443C2×#121C22×C13911yescharacteristic
444C2×#121C22×C13911yescharacteristic
445C2×C4×D4C22×C13911yescharacteristic
446C2×C4×D4C22×C13911yescharacteristic
447#469—24no—
448#465—24no—
449#463—24no—
450#435—24no—
451C2×#106C22×C13911yescharacteristic
452C2×#106C22×C13911yescharacteristic
453C2×C4⋊C8C22×C13911yescharacteristic
454C2×#103C22×C13911yescharacteristic
455C2×#103C22×C13911yescharacteristic
456C2×#103C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×#102C22×C13911yescharacteristic
459C2×#102C22×C13911yescharacteristic
460C2×#102C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×C22⋊C8C22×C13911yescharacteristic
463C2×C22⋊C8C22×C13911yescharacteristic
464C2×#97C22×C13911yescharacteristic
465#399—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#390—21no—
470#390—21no—
471#384C22×C13911yescharacteristic
472#380—21no—
473#380C22×C13911yescharacteristic
474#380C22×C13911yescharacteristic
475C4×C4⋊C4C22×C13911yescharacteristic
476#340C22×C13911yescharacteristic
477#340C22×C13911yescharacteristic
478#340C22×C13911yescharacteristic
479#340C22×C13911yescharacteristic
480C22×Q8C23×C13911yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C13911yescharacteristic
486C22×D4C23×C13911yescharacteristic
487C22×D4C23×C13911yescharacteristic
488C23×C4—21no—
489C23×C4C23×C13911yescharacteristic
490C23×C4C23×C13911yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C13911yescharacteristic
504C22×C8C23×C13911yescharacteristic
505C22×C8C23×C13911yescharacteristic
506C22×C8C23×C13911yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C13911yescharacteristic
531C2×C4⋊C4C23×C13911yescharacteristic
532C2×C4⋊C4C23×C13911yescharacteristic
533C2×C4⋊C4C23×C13911yescharacteristic
534C2×C4⋊C4C23×C13911yescharacteristic
535C2×C4⋊C4C23×C13911yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C13911yescharacteristic
548C2×C22⋊C4D4×C13911yescharacteristic
549C2×C42—21no—
550C2×C42C23×C13911yescharacteristic
551#106—22no—
552#106—22no—
553C4⋊C8D4×C13914yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C13914yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C13911yescharacteristic
571C24C2×D4×C13911yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C13912yes—
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—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C13911yescharacteristic
627C22×C4C2×D4×C13911yescharacteristic
628C22×C4C2×D4×C13911yescharacteristic
629C22×C4C2×D4×C13911yescharacteristic
630C22×C4C24×C13911yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C13912yes—
645C2×C8C2×D4×C13912yes—
646C2×C8C2×D4×C13912yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C13912yes—
661C4⋊C4#41×C13912yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C13912yes—
677C42#41×C13912yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C13912yes—
706C23C22×D4×C13911yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
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—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4#121×C13912yes—
762C2×C4#121×C13912yes—
763C2×C4C22×D4×C13911yescharacteristic
764C2×C4C22×D4×C13911yescharacteristic
765C2×C4C2×#41×C13911yescharacteristic
766C2×C4C2×#41×C13911yescharacteristic
767C2×C4H(5,𝔽2)×C13911yescharacteristic
768C2×C4H(5,𝔽2)×C13911yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C13911yescharacteristic
802C22D42×C13911yescharacteristic
803C22#546×C13911yescharacteristic
804C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
805C22#575×C13911yescharacteristic
806C22#577×C13911yescharacteristic
807C22#577×C13911yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#532×C13911yescharacteristic
819C4#540×C13911yescharacteristic
820C4D42×C13911yescharacteristic
821C4#550×C13911yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2#2428×C13911yescharacteristic
827C2#3055×C13911yescharacteristic
828C2#3060×C13911yescharacteristic
829C2#3265×C13911yescharacteristic
830C2#3267×C13911yescharacteristic
831C2#3306×C13911yescharacteristic
832C2#3321×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×#465×C139C2semidirect
3. C2×#463×C139C2semidirect
4. C2×#435×C139C2semidirect
5. #2540×C139C2semidirect
6. #2537×C139C2semidirect
7. #2035×C139C2semidirect
8. #2034×C139C2semidirect
9. #2000×C139C2semidirect
10. #1999×C139C2semidirect
11. #1959×C139C2semidirect
12. #1948×C139C2semidirect
13. #1894×C139C2semidirect
14. #1893×C139C2semidirect
15. #1762×C139C2semidirect
136. C4⋊C8×C139D4semidirect
144. #102×C139D4semidirect
416. #25401C139direct (N × H)
417. C139#25401direct (N × H)
418. C2×#469C2×C139semidirect
419. C2×#465C2×C139semidirect
420. C2×#463C2×C139semidirect
421. C2×#435C2×C139semidirect
422. #2540C2×C139semidirect
423. #2537C2×C139semidirect
424. #2035C2×C139semidirect
425. #2034C2×C139semidirect
426. #2000C2×C139semidirect
427. #1999C2×C139semidirect
428. #1959C2×C139semidirect
429. #1948C2×C139semidirect
430. #1894C2×C139semidirect
431. #1893C2×C139semidirect
432. #1762C2×C139semidirect
553. C4⋊C8D4×C139semidirect
561. #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×#465×C1392
C2×#463×C1392
C2×#435×C1392
#2540×C1392
#2537×C1392
#2035×C1392
#2034×C1392
#2000×C1392
#1999×C1392
#1959×C1392
#1948×C1392
#1894×C1392
#1893×C1392
#1762×C1392
#25401139