Finite Group Databasebeta

← C139×#22423 #48017019

Subgroups — C139×#22423 #48017019

Order 35584.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C139C211yesmaximal, characteristic
2C2×#435×C139C211yesmaximal, characteristic, complemented
3C2×#418×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2352×C139C211yesmaximal, characteristic, complemented
6#1982×C139C211yesmaximal, characteristic, complemented
7#1961×C139C211yesmaximal, characteristic, complemented
8#1895×C139C211yesmaximal, characteristic, complemented
9#1893×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1804×C139C211yesmaximal, characteristic, complemented
13#1786×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139—21no—
17C23×D4×C139C2211yescharacteristic
18C23×D4×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic, complemented
20C23×C8×C139C2211yescharacteristic, complemented
21D42×C139—24no—
22D42×C139C418yescomplemented
23C2×#127×C139C2211yescharacteristic
24C2×#121×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#120×C139—21no—
28C2×#120×C139—21no—
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×#117×C139C2211yescharacteristic, complemented
32C22×C4⋊C4×C139C2211yescharacteristic, complemented
33#435×C139—24no—
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35#418×C139—24no—
36C2×#102×C139—24no—
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic, complemented
42C2×#102×C139C2211yescharacteristic, complemented
43C2×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic, complemented
47C2×#102×C139C2211yescharacteristic, complemented
48C2×#102×C139C2211yescharacteristic, complemented
49C2×C22⋊C8×C139C2211yescharacteristic, complemented
50C2×C22⋊C8×C139C2211yescharacteristic, complemented
51C2×#97×C139C2211yescharacteristic, complemented
52#388×C139—21no—
53#387×C139—21no—
54#386×C139—21no—
55#382×C139C2211yescharacteristic, complemented
56#380×C139C2211yescharacteristic, complemented
57#380×C139C2211yescharacteristic, complemented
58C4×C4⋊C4×C139C2211yescharacteristic, complemented
59C4×C22⋊C4×C139—21no—
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64C25×C139—21no—
65C25×C139—21no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—22no—
69C22×D4×C139—22no—
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—28no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—22no—
77C22×D4×C139—22no—
78C22×D4×C139—21no—
79C22×D4×C139—41no—
80C22×D4×C139—41no—
81C22×D4×C139—41no—
82C22×D4×C139—41no—
83C22×D4×C139—44no—
84C22×D4×C139—44no—
85C22×D4×C139C2×C414yes—
86C22×D4×C139C2×C414yescomplemented
87C22×D4×C139D411yescharacteristic
88C22×D4×C139C2311yescharacteristic
89C22×D4×C139C2311yescharacteristic
90C22×D4×C139C2311yescharacteristic
91C23×C4×C139—21no—
92C23×C4×C139—21no—
93C23×C4×C139C2311yescharacteristic
94C23×C4×C139C2311yescharacteristic
95C2×M16×C139—22no—
96C2×M16×C139—22no—
97C2×M16×C139—41no—
98C22×C8×C139—22no—
99C22×C8×C139—22no—
100C22×C8×C139—41no—
101C22×C8×C139C2311yescharacteristic
102C22×C8×C139C2311yescharacteristic
103C22×C8×C139C2311yescharacteristic
104C22×C8×C139C2311yescharacteristic
105#127×C139—22no—
106#127×C139C2×C414yescomplemented
107#121×C139—22no—
108#121×C139—22no—
109#121×C139—28no—
110#121×C139C2×C414yes—
111#121×C139C2×C414yescomplemented
112#120×C139—28no—
113#120×C139—28no—
114C4×D4×C139—22no—
115C4×D4×C139C2×C414yes—
116C4×D4×C139C2×C414yescomplemented
117C4×D4×C139D414yes—
118#117×C139—22no—
119#117×C139—41no—
120C2×C4⋊C4×C139—22no—
121C2×C4⋊C4×C139—21no—
122C2×C4⋊C4×C139—41no—
123C2×C4⋊C4×C139D411yescharacteristic
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C4⋊C4×C139C2311yescharacteristic
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139D411yescharacteristic
136C2×C22⋊C4×C139D411yescharacteristic
137C2×C42×C139—21no—
138C2×C42×C139—21no—
139C2×C42×C139C2311yescharacteristic
140C4⋊C8×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139—22no—
146#102×C139—22no—
147#102×C139—22no—
148#102×C139—41no—
149#102×C139—41no—
150#102×C139—41no—
151#102×C139—41no—
152#102×C139D414yescomplemented
153C22⋊C8×C139—22no—
154C22⋊C8×C139—22no—
155#97×C139—22no—
156#95×C139—21no—
157#95×C139—21no—
158#95×C139—21no—
159#95×C139—21no—
160#95×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—24no—
165C24×C139—24no—
166C24×C139—42no—
167C24×C139—42no—
168C24×C139—42no—
169C24×C139—42no—
170C24×C139—42no—
171C24×C139—42no—
172C24×C139—42no—
173C24×C139—42no—
174C24×C139—81no—
175C24×C139—81no—
176C24×C139—81no—
177C24×C139—81no—
178C24×C139C2×D411yescharacteristic
179C24×C139C2×D411yescharacteristic
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—28no—
183C2×D4×C139—28no—
184C2×D4×C139—24no—
185C2×D4×C139—24no—
186C2×D4×C139—24no—
187C2×D4×C139—24no—
188C2×D4×C139—24no—
189C2×D4×C139—24no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—44no—
204C2×D4×C139—44no—
205C2×D4×C139—44no—
206C2×D4×C139—44no—
207C2×D4×C139—44no—
208C2×D4×C139—44no—
209C2×D4×C139—42no—
210C2×D4×C139—42no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—42no—
215C2×D4×C139—432no—
216C2×D4×C139—42no—
217C2×D4×C139—42no—
218C2×D4×C139—42no—
219C2×D4×C139—42no—
220C2×D4×C139—81no—
221C2×D4×C139—81no—
222C2×D4×C139C22⋊C414yes—
223C2×D4×C139C22×C412yes—
224C2×D4×C139C22×C412yes—
225C2×D4×C139C22×C412yes—
226C2×D4×C139C2×D412yes—
227C2×D4×C139#4112yes—
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—21no—
237C22×C4×C139—21no—
238C22×C4×C139—24no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—42no—
243C22×C4×C139—42no—
244C22×C4×C139—42no—
245C22×C4×C139—42no—
246C22×C4×C139—81no—
247C22×C4×C139C22×C412yes—
248C22×C4×C139C22×C412yes—
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2×D411yescharacteristic
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139C2×D411yescharacteristic
253C22×C4×C139C2×D412yes—
254C22×C4×C139C2×D412yes—
255C22×C4×C139C2411yescharacteristic
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×C139—21no—
268C2×C8×C139—44no—
269C2×C8×C139C2×D412yescomplemented
270C4⋊C4×C139—21no—
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—42no—
279C4⋊C4×C139C22⋊C414yes—
280C4⋊C4×C139C22×C412yes—
281C4⋊C4×C139C2×D412yescomplemented
282C22⋊C4×C139—24no—
283C22⋊C4×C139—24no—
284C22⋊C4×C139—24no—
285C22⋊C4×C139—42no—
286C22⋊C4×C139—42no—
287C22⋊C4×C139—81no—
288C22⋊C4×C139C22⋊C414yes—
289C22⋊C4×C139C22⋊C414yes—
290C42×C139—42no—
291C42×C139—81no—
292C42×C139C22×C412yes—
293C42×C139C2×D412yes—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—21no—
297C23×C139—21no—
298C23×C139—22no—
299C23×C139—21no—
300C23×C139—22no—
301C23×C139—21no—
302C23×C139—22no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—21no—
307C23×C139—22no—
308C23×C139—22no—
309C23×C139—48no—
310C23×C139—48no—
311C23×C139—48no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—41no—
321C23×C139—41no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—48no—
329C23×C139—84no—
330C23×C139—84no—
331C23×C139—84no—
332C23×C139—84no—
333C23×C139—84no—
334C23×C139—84no—
335C23×C139—84no—
336C23×C139—84no—
337C23×C139—84no—
338C23×C139—84no—
339C23×C139C2×C22⋊C412yes—
340C23×C139C2×C22⋊C412yes—
341C23×C139AGL(1,ℤ/8)12yes—
342C23×C139AGL(1,ℤ/8)12yes—
343C23×C139C22×D411yescharacteristic
344D4×C139—28no—
345D4×C139—22no—
346D4×C139—22no—
347D4×C139—22no—
348D4×C139—22no—
349D4×C139—22no—
350D4×C139—22no—
351D4×C139—22no—
352D4×C139—48no—
353D4×C139—48no—
354D4×C139—48no—
355D4×C139—48no—
356D4×C139—48no—
357D4×C139—41no—
358D4×C139—41no—
359D4×C139—41no—
360D4×C139—41no—
361D4×C139—84no—
362D4×C139C4×D414yes—
363C2×C4×C139—21no—
364C2×C4×C139—21no—
365C2×C4×C139—21no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—21no—
369C2×C4×C139—21no—
370C2×C4×C139—21no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—22no—
374C2×C4×C139—22no—
375C2×C4×C139—22no—
376C2×C4×C139—22no—
377C2×C4×C139—22no—
378C2×C4×C139—22no—
379C2×C4×C139—22no—
380C2×C4×C139—22no—
381C2×C4×C139—48no—
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—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—84no—
396C2×C4×C139C2×C22⋊C412yes—
397C2×C4×C139C2×C22⋊C412yes—
398C2×C4×C139C2×C22⋊C412yes—
399C2×C4×C139C2×C22⋊C412yes—
400C2×C4×C139C23×C411yescharacteristic
401C2×C4×C139C22×D411yescharacteristic
402C2×C4×C139C22×D411yescharacteristic
403C2×C4×C139C2×#4111yescharacteristic
404C2×C4×C139H(5,𝔽2)11yescharacteristic
405C2×C4×C139H(5,𝔽2)11yescharacteristic
406C8×C139—22no—
407C8×C139—41no—
408C8×C139—41no—
409C8×C139—41no—
410C22×C139—22no—
411C22×C139—22no—
412C22×C139—22no—
413C22×C139—22no—
414C22×C139—22no—
415C22×C139—22no—
416C22×C139—22no—
417C22×C139—24no—
418C22×C139—22no—
419C22×C139—22no—
420C22×C139—42no—
421C22×C139—42no—
422C22×C139—41no—
423C22×C139—42no—
424C22×C139—41no—
425C22×C139—42no—
426C22×C139—41no—
427C22×C139—42no—
428C22×C139—41no—
429C22×C139—42no—
430C22×C139—42no—
431C22×C139—42no—
432C22×C139—42no—
433C22×C139—42no—
434C22×C139—42no—
435C22×C139—42no—
436C22×C139—816no—
437C22×C139—816no—
438C22×C139—81no—
439C22×C139—81no—
440C22×C139—81no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139#41814yescomplemented
447C22×C139C22×C22⋊C411yescharacteristic
448C22×C139D4211yescharacteristic
449C22×C139#54611yescharacteristic
450C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C139#57611yescharacteristic
453C22×C139#57711yescharacteristic
454C4×C139—22no—
455C4×C139—22no—
456C4×C139—22no—
457C4×C139—22no—
458C4×C139—42no—
459C4×C139—42no—
460C4×C139—81no—
461C4×C139—81no—
462C4×C139—81no—
463C4×C139C2×C4×D411yescharacteristic
464C4×C139#51811yescharacteristic
465C4×C139D4211yescharacteristic
466C4×C139#54611yescharacteristic
467C2×C139—24no—
468C2×C139—42no—
469C2×C139—44no—
470C2×C139—82no—
471C2×C139—82no—
472C2×C139D4×C22⋊C411yescharacteristic
473C2×C139C2×#41811yescharacteristic
474C2×C139#289711yescharacteristic
475C2×C139#326411yescharacteristic
476C2×C139#326511yescharacteristic
477C2×C139#331011yescharacteristic
478C2×C139#331811yescharacteristic
479#22423C13911yesmaximal, characteristic, direct product factor, Sylow
480C139#2242311yescharacteristic, direct product factor, Sylow
481C2×D42C2×C13911yescharacteristic
482C2×#435C2×C13911yescharacteristic, complemented
483C2×#418C2×C13911yescharacteristic, complemented
484C22×#102C2×C13911yescharacteristic, complemented
485#2352C2×C13911yescharacteristic, complemented
486#1982C2×C13911yescharacteristic, complemented
487#1961C2×C13911yescharacteristic, complemented
488#1895C2×C13911yescharacteristic, complemented
489#1893C2×C13911yescharacteristic, complemented
490#1875C2×C13911yescharacteristic, complemented
491#1874C2×C13911yescharacteristic, complemented
492#1804C2×C13911yescharacteristic, complemented
493#1786C2×C13911yescharacteristic, complemented
494#1786C2×C13911yescharacteristic, complemented
495#1762C2×C13911yescharacteristic, complemented
496C23×D4—21no—
497C23×D4C22×C13911yescharacteristic
498C23×D4C22×C13911yescharacteristic
499C22×M16C22×C13911yescharacteristic, complemented
500C23×C8C22×C13911yescharacteristic, complemented
501D42—24no—
502D42C4×C13918yescomplemented
503C2×#127C22×C13911yescharacteristic
504C2×#121—21no—
505C2×#121C22×C13911yescharacteristic
506C2×#121C22×C13911yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4C22×C13911yescharacteristic
510C2×C4×D4C22×C13911yescharacteristic
511C2×#117C22×C13911yescharacteristic, complemented
512C22×C4⋊C4C22×C13911yescharacteristic, complemented
513#435—24no—
514C2×C4⋊C8C22×C13911yescharacteristic, complemented
515#418—24no—
516C2×#102—24no—
517C2×#102C22×C13911yescharacteristic
518C2×#102C22×C13911yescharacteristic
519C2×#102C22×C13911yescharacteristic
520C2×#102C22×C13911yescharacteristic
521C2×#102C22×C13911yescharacteristic, complemented
522C2×#102C22×C13911yescharacteristic, complemented
523C2×#102C22×C13911yescharacteristic, complemented
524C2×#102C22×C13911yescharacteristic, complemented
525C2×#102C22×C13911yescharacteristic, complemented
526C2×#102C22×C13911yescharacteristic, complemented
527C2×#102C22×C13911yescharacteristic, complemented
528C2×#102C22×C13911yescharacteristic, complemented
529C2×C22⋊C8C22×C13911yescharacteristic, complemented
530C2×C22⋊C8C22×C13911yescharacteristic, complemented
531C2×#97C22×C13911yescharacteristic, complemented
532#388—21no—
533#387—21no—
534#386—21no—
535#382C22×C13911yescharacteristic, complemented
536#380C22×C13911yescharacteristic, complemented
537#380C22×C13911yescharacteristic, complemented
538C4×C4⋊C4C22×C13911yescharacteristic, complemented
539C4×C22⋊C4—21no—
540#340C22×C13911yescharacteristic, complemented
541#340C22×C13911yescharacteristic, complemented
542#340C22×C13911yescharacteristic, complemented
543#340C22×C13911yescharacteristic, complemented
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C13914yes—
566C22×D4C2×C4×C13914yescomplemented
567C22×D4D4×C13911yescharacteristic
568C22×D4C23×C13911yescharacteristic
569C22×D4C23×C13911yescharacteristic
570C22×D4C23×C13911yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C13911yescharacteristic
574C23×C4C23×C13911yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C13911yescharacteristic
582C22×C8C23×C13911yescharacteristic
583C22×C8C23×C13911yescharacteristic
584C22×C8C23×C13911yescharacteristic
585#127—22no—
586#127C2×C4×C13914yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C13914yes—
591#121C2×C4×C13914yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C13914yes—
596C4×D4C2×C4×C13914yescomplemented
597C4×D4D4×C13914yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C13911yescharacteristic
604C2×C4⋊C4C23×C13911yescharacteristic
605C2×C4⋊C4C23×C13911yescharacteristic
606C2×C4⋊C4C23×C13911yescharacteristic
607C2×C4⋊C4C23×C13911yescharacteristic
608C2×C4⋊C4C23×C13911yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C13911yescharacteristic
616C2×C22⋊C4D4×C13911yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C13911yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C13914yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C13911yescharacteristic
659C24C2×D4×C13911yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C13914yes—
703C2×D4C22×C4×C13912yes—
704C2×D4C22×C4×C13912yes—
705C2×D4C22×C4×C13912yes—
706C2×D4C2×D4×C13912yes—
707C2×D4#41×C13912yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C13912yes—
728C22×C4C22×C4×C13912yes—
729C22×C4C2×D4×C13911yescharacteristic
730C22×C4C2×D4×C13911yescharacteristic
731C22×C4C2×D4×C13911yescharacteristic
732C22×C4C2×D4×C13911yescharacteristic
733C22×C4C2×D4×C13912yes—
734C22×C4C2×D4×C13912yes—
735C22×C4C24×C13911yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C13912yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C13914yes—
760C4⋊C4C22×C4×C13912yes—
761C4⋊C4C2×D4×C13912yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C13914yes—
769C22⋊C4C22⋊C4×C13914yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C13912yes—
773C42C2×D4×C13912yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C13912yes—
820C23C2×C22⋊C4×C13912yes—
821C23AGL(1,ℤ/8)×C13912yes—
822C23AGL(1,ℤ/8)×C13912yes—
823C23C22×D4×C13911yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C13914yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C13912yes—
877C2×C4C2×C22⋊C4×C13912yes—
878C2×C4C2×C22⋊C4×C13912yes—
879C2×C4C2×C22⋊C4×C13912yes—
880C2×C4C23×C4×C13911yescharacteristic
881C2×C4C22×D4×C13911yescharacteristic
882C2×C4C22×D4×C13911yescharacteristic
883C2×C4C2×#41×C13911yescharacteristic
884C2×C4H(5,𝔽2)×C13911yescharacteristic
885C2×C4H(5,𝔽2)×C13911yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#418×C13914yescomplemented
927C22C22×C22⋊C4×C13911yescharacteristic
928C22D42×C13911yescharacteristic
929C22#546×C13911yescharacteristic
930C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
931C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
932C22#576×C13911yescharacteristic
933C22#577×C13911yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C13911yescharacteristic
944C4#518×C13911yescharacteristic
945C4D42×C13911yescharacteristic
946C4#546×C13911yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C13911yescharacteristic
953C2C2×#418×C13911yescharacteristic
954C2#2897×C13911yescharacteristic
955C2#3264×C13911yescharacteristic
956C2#3265×C13911yescharacteristic
957C2#3310×C13911yescharacteristic
958C2#3318×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×D42×C139C2
LCSG ▷ C2×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
2. C2×#435×C139C2semidirect
3. C2×#418×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2352×C139C2semidirect
6. #1982×C139C2semidirect
7. #1961×C139C2semidirect
8. #1895×C139C2semidirect
9. #1893×C139C2semidirect
10. #1875×C139C2semidirect
11. #1874×C139C2semidirect
12. #1804×C139C2semidirect
13. #1786×C139C2semidirect
14. #1786×C139C2semidirect
15. #1762×C139C2semidirect
19. C22×M16×C139C22semidirect
20. C23×C8×C139C22semidirect
22. D42×C139C4semidirect
31. C2×#117×C139C22semidirect
32. C22×C4⋊C4×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
41. C2×#102×C139C22semidirect
42. C2×#102×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
46. C2×#102×C139C22semidirect
47. C2×#102×C139C22semidirect
48. C2×#102×C139C22semidirect
49. C2×C22⋊C8×C139C22semidirect
50. C2×C22⋊C8×C139C22semidirect
51. C2×#97×C139C22semidirect
55. #382×C139C22semidirect
56. #380×C139C22semidirect
57. #380×C139C22semidirect
58. C4×C4⋊C4×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
86. C22×D4×C139C2×C4semidirect
106. #127×C139C2×C4semidirect
111. #121×C139C2×C4semidirect
116. C4×D4×C139C2×C4semidirect
152. #102×C139D4semidirect
269. C2×C8×C139C2×D4semidirect
281. C4⋊C4×C139C2×D4semidirect
446. C22×C139#418semidirect
479. #22423C139direct (N × H)
480. C139#22423direct (N × H)
482. C2×#435C2×C139semidirect
483. C2×#418C2×C139semidirect
484. C22×#102C2×C139semidirect
485. #2352C2×C139semidirect
486. #1982C2×C139semidirect
487. #1961C2×C139semidirect
488. #1895C2×C139semidirect
489. #1893C2×C139semidirect
490. #1875C2×C139semidirect
491. #1874C2×C139semidirect
492. #1804C2×C139semidirect
493. #1786C2×C139semidirect
494. #1786C2×C139semidirect
495. #1762C2×C139semidirect
499. C22×M16C22×C139semidirect
500. C23×C8C22×C139semidirect
502. D42C4×C139semidirect
511. C2×#117C22×C139semidirect
512. C22×C4⋊C4C22×C139semidirect
514. C2×C4⋊C8C22×C139semidirect
521. C2×#102C22×C139semidirect
522. C2×#102C22×C139semidirect
523. C2×#102C22×C139semidirect
524. C2×#102C22×C139semidirect
525. C2×#102C22×C139semidirect
526. C2×#102C22×C139semidirect
527. C2×#102C22×C139semidirect
528. C2×#102C22×C139semidirect
529. C2×C22⋊C8C22×C139semidirect
530. C2×C22⋊C8C22×C139semidirect
531. C2×#97C22×C139semidirect
535. #382C22×C139semidirect
536. #380C22×C139semidirect
537. #380C22×C139semidirect
538. C4×C4⋊C4C22×C139semidirect
540. #340C22×C139semidirect
541. #340C22×C139semidirect
542. #340C22×C139semidirect
543. #340C22×C139semidirect
566. C22×D4C2×C4×C139semidirect
586. #127C2×C4×C139semidirect
591. #121C2×C4×C139semidirect
596. C4×D4C2×C4×C139semidirect
632. #102D4×C139semidirect
749. C2×C8C2×D4×C139semidirect
761. C4⋊C4C2×D4×C139semidirect
926. C22#418×C139semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1392
C2×#435×C1392
C2×#418×C1392
C22×#102×C1392
#2352×C1392
#1982×C1392
#1961×C1392
#1895×C1392
#1893×C1392
#1875×C1392
#1874×C1392
#1804×C1392
#1786×C1392
#1762×C1392
#22423139