Finite Group Databasebeta

← C139×#24136 #48018732

Subgroups — C139×#24136 #48018732

Order 35584.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C139C211yesmaximal, characteristic, complemented
2C2×#478×C139C211yesmaximal, characteristic, complemented
3C2×#442×C139C211yesmaximal, characteristic, complemented
4#2537×C139C211yesmaximal, characteristic, complemented
5#2034×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#1999×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1992×C139C211yesmaximal, characteristic, complemented
10#1955×C139C211yesmaximal, characteristic, complemented
11#1875×C139C211yesmaximal, characteristic, complemented
12#1874×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1853×C139C211yesmaximal, characteristic, complemented
15#1802×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17#553×C139—24no—
18#553×C139—24no—
19C2×#126×C139—21no—
20C2×#125×C139C2211yescharacteristic
21C2×#123×C139—21no—
22C2×#121×C139—21no—
23C2×#121×C139—21no—
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×C4×D4×C139—21no—
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×#117×C139C2211yescharacteristic
33C22×C4⋊C4×C139C2211yescharacteristic
34#478×C139—24no—
35#442×C139—24no—
36C2×#107×C139C2211yescharacteristic
37C2×#106×C139C2211yescharacteristic
38C2×#106×C139C2211yescharacteristic
39C2×C4⋊C8×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50C2×#97×C139C2211yescharacteristic
51#394×C139—21no—
52#394×C139—21no—
53#384×C139C2211yescharacteristic
54#380×C139—21no—
55#380×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139D411yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C23×C4×C139—21no—
71C23×C4×C139—21no—
72C23×C4×C139—21no—
73C23×C4×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—22no—
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82#126×C139—28no—
83#125×C139—22no—
84#125×C139D414yescomplemented
85#123×C139—28no—
86#121×C139—28no—
87#121×C139—22no—
88#121×C139—22no—
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—41no—
94#121×C139—41no—
95#121×C139—44no—
96C4×D4×C139—28no—
97C4×D4×C139—22no—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102C4×D4×C139D414yescomplemented
103#117×C139—22no—
104#117×C139—22no—
105C2×C4⋊C4×C139—21no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—22no—
109C2×C4⋊C4×C139—22no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139D411yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
129C2×C22⋊C4×C139D411yescharacteristic
130C2×C42×C139—21no—
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133#106×C139—22no—
134#106×C139—22no—
135C4⋊C8×C139—22no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—41no—
141#102×C139—41no—
142C22⋊C8×C139—22no—
143C22⋊C8×C139—22no—
144C22⋊C8×C139—41no—
145C22⋊C8×C139—41no—
146#97×C139—22no—
147#95×C139—21no—
148#95×C139—21no—
149C24×C139—21no—
150C24×C139—21no—
151C24×C139C2×D411yescharacteristic
152C24×C139C2×D411yescharacteristic
153C2×D4×C139—24no—
154C2×D4×C139—22no—
155C2×D4×C139—24no—
156C2×D4×C139—22no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
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—41no—
168C2×D4×C139—42no—
169C2×D4×C139—42no—
170C2×D4×C139—42no—
171C2×D4×C139—42no—
172C2×D4×C139—42no—
173C2×D4×C139—42no—
174C2×D4×C139—81no—
175C2×D4×C139—81no—
176C2×D4×C139—81no—
177C2×D4×C139—81no—
178C2×D4×C139C2×D412yes—
179C2×D4×C139#4112yes—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—24no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
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—24no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—42no—
201C22×C4×C139—42no—
202C22×C4×C139—42no—
203C22×C4×C139—81no—
204C22×C4×C139—81no—
205C22×C4×C139—81no—
206C22×C4×C139—81no—
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2411yescharacteristic
212D8×C139—28no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
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#4112yes—
225C4⋊C4×C139—24no—
226C4⋊C4×C139—24no—
227C4⋊C4×C139—24no—
228C4⋊C4×C139—22no—
229C4⋊C4×C139—21no—
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—81no—
240C4⋊C4×C139C2×D412yes—
241C4⋊C4×C139C2×D412yes—
242C4⋊C4×C139C2×D412yes—
243C22⋊C4×C139—24no—
244C22⋊C4×C139—24no—
245C22⋊C4×C139—24no—
246C22⋊C4×C139—24no—
247C22⋊C4×C139—22no—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C42×C139—24no—
255C42×C139C2×D412yes—
256C42×C139C2×D412yes—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—22no—
265C23×C139—22no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—41no—
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×C139AGL(1,ℤ/8)12yes—
285C23×C139C22×D411yescharacteristic
286D4×C139—22no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—22no—
290D4×C139—44no—
291D4×C139—48no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—84no—
297D4×C139—84no—
298D4×C139—84no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—22no—
305C2×C4×C139—22no—
306C2×C4×C139—21no—
307C2×C4×C139—22no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
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—84no—
336C2×C4×C139—84no—
337C2×C4×C139—84no—
338C2×C4×C139#12012yes—
339C2×C4×C139#12012yes—
340C2×C4×C139C22×D411yescharacteristic
341C2×C4×C139C22×D411yescharacteristic
342C2×C4×C139C2×#4111yescharacteristic
343C2×C4×C139C2×#4111yescharacteristic
344C2×C4×C139H(5,𝔽2)11yescharacteristic
345C2×C4×C1392−1+411yescharacteristic
346C8×C139—22no—
347C8×C139—41no—
348C8×C139—41no—
349C8×C139—41no—
350C22×C139—22no—
351C22×C139—22no—
352C22×C139—22no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—41no—
356C22×C139—41no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—42no—
362C22×C139—41no—
363C22×C139—42no—
364C22×C139—42no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—42no—
368C22×C139—41no—
369C22×C139—42no—
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×C139C2×#12011yescharacteristic
379C22×C139#54611yescharacteristic
380C22×C139#54711yescharacteristic
381C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C139#57511yescharacteristic
383C22×C139#57611yescharacteristic
384C22×C139#57711yescharacteristic
385C4×C139—22no—
386C4×C139—22no—
387C4×C139—41no—
388C4×C139—41no—
389C4×C139—42no—
390C4×C139—42no—
391C4×C139—42no—
392C4×C139—81no—
393C4×C139—81no—
394C4×C139—81no—
395C4×C139#52511yescharacteristic
396C4×C139#53711yescharacteristic
397C4×C139#54811yescharacteristic
398C4×C139#55011yescharacteristic
399C2×C139—42no—
400C2×C139—81no—
401C2×C139—82no—
402C2×C139—82no—
403C2×C139#240711yescharacteristic
404C2×C139#300611yescharacteristic
405C2×C139#301211yescharacteristic
406C2×C139#330711yescharacteristic
407C2×C139#331811yescharacteristic
408C2×C139#334511yescharacteristic
409C2×C139#334711yescharacteristic
410#24136C13911yesmaximal, characteristic, direct product factor, Sylow
411C139#2413611yescharacteristic, direct product factor, Sylow
412C2×#553C2×C13911yescharacteristic, complemented
413C2×#478C2×C13911yescharacteristic, complemented
414C2×#442C2×C13911yescharacteristic, complemented
415#2537C2×C13911yescharacteristic, complemented
416#2034C2×C13911yescharacteristic, complemented
417#2033C2×C13911yescharacteristic, complemented
418#1999C2×C13911yescharacteristic, complemented
419#1999C2×C13911yescharacteristic, complemented
420#1992C2×C13911yescharacteristic, complemented
421#1955C2×C13911yescharacteristic, complemented
422#1875C2×C13911yescharacteristic, complemented
423#1874C2×C13911yescharacteristic, complemented
424#1854C2×C13911yescharacteristic, complemented
425#1853C2×C13911yescharacteristic, complemented
426#1802C2×C13911yescharacteristic, complemented
427C22×D8C22×C13911yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C13911yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C13911yescharacteristic
436C2×#121C22×C13911yescharacteristic
437C2×#121C22×C13911yescharacteristic
438C2×#121C22×C13911yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C13911yescharacteristic
441C2×C4×D4C22×C13911yescharacteristic
442C2×C4×D4C22×C13911yescharacteristic
443C2×#117C22×C13911yescharacteristic
444C22×C4⋊C4C22×C13911yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C13911yescharacteristic
448C2×#106C22×C13911yescharacteristic
449C2×#106C22×C13911yescharacteristic
450C2×C4⋊C8C22×C13911yescharacteristic
451C2×#102C22×C13911yescharacteristic
452C2×#102C22×C13911yescharacteristic
453C2×#102C22×C13911yescharacteristic
454C2×#102C22×C13911yescharacteristic
455C2×#102C22×C13911yescharacteristic
456C2×#102C22×C13911yescharacteristic
457C2×C22⋊C8C22×C13911yescharacteristic
458C2×C22⋊C8C22×C13911yescharacteristic
459C2×C22⋊C8C22×C13911yescharacteristic
460C2×C22⋊C8C22×C13911yescharacteristic
461C2×#97C22×C13911yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C13911yescharacteristic
465#380—21no—
466#380C22×C13911yescharacteristic
467#380C22×C13911yescharacteristic
468#340C22×C13911yescharacteristic
469#340C22×C13911yescharacteristic
470#340C22×C13911yescharacteristic
471#340C22×C13911yescharacteristic
472#340C22×C13911yescharacteristic
473#340C22×C13911yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C13911yescharacteristic
479C22×D4C23×C13911yescharacteristic
480C22×D4C23×C13911yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C13911yescharacteristic
485C23×C4C23×C13911yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C13911yescharacteristic
490C22×C8C23×C13911yescharacteristic
491C22×C8C23×C13911yescharacteristic
492C22×C8C23×C13911yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C13914yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C13914yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C13911yescharacteristic
524C2×C4⋊C4C23×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⋊C4D4×C13911yescharacteristic
540C2×C22⋊C4D4×C13911yescharacteristic
541C2×C42—21no—
542C2×C42C23×C13911yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C13911yescharacteristic
563C24C2×D4×C13911yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C13912yes—
590C2×D4#41×C13912yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C13911yescharacteristic
619C22×C4C2×D4×C13911yescharacteristic
620C22×C4C2×D4×C13911yescharacteristic
621C22×C4C2×D4×C13911yescharacteristic
622C22×C4C24×C13911yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C13912yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C13912yes—
652C4⋊C4C2×D4×C13912yes—
653C4⋊C4C2×D4×C13912yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C13912yes—
667C42C2×D4×C13912yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C13912yes—
696C23C22×D4×C13911yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
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—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C13912yes—
750C2×C4#120×C13912yes—
751C2×C4C22×D4×C13911yescharacteristic
752C2×C4C22×D4×C13911yescharacteristic
753C2×C4C2×#41×C13911yescharacteristic
754C2×C4C2×#41×C13911yescharacteristic
755C2×C4H(5,𝔽2)×C13911yescharacteristic
756C2×C42−1+4×C13911yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C13911yescharacteristic
790C22#546×C13911yescharacteristic
791C22#547×C13911yescharacteristic
792C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
793C22#575×C13911yescharacteristic
794C22#576×C13911yescharacteristic
795C22#577×C13911yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C13911yescharacteristic
807C4#537×C13911yescharacteristic
808C4#548×C13911yescharacteristic
809C4#550×C13911yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2#2407×C13911yescharacteristic
815C2#3006×C13911yescharacteristic
816C2#3012×C13911yescharacteristic
817C2#3307×C13911yescharacteristic
818C2#3318×C13911yescharacteristic
819C2#3345×C13911yescharacteristic
820C2#3347×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×#553×C139C2semidirect
2. C2×#478×C139C2semidirect
3. C2×#442×C139C2semidirect
4. #2537×C139C2semidirect
5. #2034×C139C2semidirect
6. #2033×C139C2semidirect
7. #1999×C139C2semidirect
8. #1999×C139C2semidirect
9. #1992×C139C2semidirect
10. #1955×C139C2semidirect
11. #1875×C139C2semidirect
12. #1874×C139C2semidirect
13. #1854×C139C2semidirect
14. #1853×C139C2semidirect
15. #1802×C139C2semidirect
84. #125×C139D4semidirect
102. C4×D4×C139D4semidirect
410. #24136C139direct (N × H)
411. C139#24136direct (N × H)
412. C2×#553C2×C139semidirect
413. C2×#478C2×C139semidirect
414. C2×#442C2×C139semidirect
415. #2537C2×C139semidirect
416. #2034C2×C139semidirect
417. #2033C2×C139semidirect
418. #1999C2×C139semidirect
419. #1999C2×C139semidirect
420. #1992C2×C139semidirect
421. #1955C2×C139semidirect
422. #1875C2×C139semidirect
423. #1874C2×C139semidirect
424. #1854C2×C139semidirect
425. #1853C2×C139semidirect
426. #1802C2×C139semidirect
495. #125D4×C139semidirect
513. C4×D4D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1392
C2×#478×C1392
C2×#442×C1392
#2537×C1392
#2034×C1392
#2033×C1392
#1999×C1392
#1992×C1392
#1955×C1392
#1875×C1392
#1874×C1392
#1854×C1392
#1853×C1392
#1802×C1392
#24136139