Finite Group Databasebeta

← C139×#23032 #48017628

Subgroups — C139×#23032 #48017628

Order 35584.

1054 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C139C211yesmaximal, characteristic
2C2×#440×C139C211yesmaximal, characteristic, complemented
3C22×#107×C139C211yesmaximal, characteristic, complemented
4#2361×C139C211yesmaximal, characteristic
5#2360×C139C211yesmaximal, characteristic, complemented
6#1973×C139C211yesmaximal, characteristic, complemented
7#1944×C139C211yesmaximal, characteristic, complemented
8#1928×C139C211yesmaximal, characteristic, complemented
9#1925×C139C211yesmaximal, characteristic, complemented
10#1874×C139C211yesmaximal, characteristic
11#1872×C139C211yesmaximal, characteristic, complemented
12#1863×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1776×C139C211yesmaximal, characteristic, complemented
15#1752×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C23×C8×C139C2211yescharacteristic
18C2×C22⋊Q8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×D4×C139—21no—
22C2×C4×D4×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2211yescharacteristic
25#465×C139C418yescomplemented
26#440×C139—24no—
27C2×#107×C139—24no—
28C2×#107×C139C2211yescharacteristic
29C2×#107×C139C2211yescharacteristic
30C2×#107×C139C2211yescharacteristic
31C2×#107×C139C2211yescharacteristic
32C2×#106×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×#97×C139C2211yescharacteristic
41C2×#97×C139C2211yescharacteristic
42#391×C139C2211yescharacteristic
43#390×C139C2211yescharacteristic
44#389×C139—21no—
45#389×C139C2211yescharacteristic
46#389×C139C2211yescharacteristic
47#388×C139—21no—
48#387×C139—21no—
49#386×C139—21no—
50#385×C139—21no—
51#385×C139—21no—
52C4×C4⋊C4×C139C2211yescharacteristic
53C4×C4⋊C4×C139C2211yescharacteristic
54C4×C22⋊C4×C139—21no—
55C4×C22⋊C4×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62C22×Q8×C139C2311yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139C2311yescharacteristic
65C23×C4×C139—21no—
66C23×C4×C139—21no—
67C23×C4×C139—21no—
68C23×C4×C139C2311yescharacteristic
69C2×SD16×C139—22no—
70C2×SD16×C139—22no—
71C2×SD16×C139C2×C414yescomplemented
72C22×C8×C139—22no—
73C22×C8×C139—22no—
74C22×C8×C139C2×C414yescomplemented
75C22×C8×C139C2311yescharacteristic
76C22×C8×C139C2311yescharacteristic
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C22⋊Q8×C139—22no—
80C22⋊Q8×C139C2×C414yescomplemented
81#121×C139—22no—
82#121×C139C2×C414yes—
83C4×Q8×C139—22no—
84C4×Q8×C139—41no—
85C4×D4×C139—22no—
86C4×D4×C139—41no—
87C4×D4×C139—44no—
88C2×C4⋊C4×C139—21no—
89C2×C4⋊C4×C139—22no—
90C2×C4⋊C4×C139—22no—
91C2×C4⋊C4×C139—21no—
92C2×C4⋊C4×C139—21no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139—41no—
97C2×C4⋊C4×C139—41no—
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139D411yescharacteristic
110C2×C22⋊C4×C139D411yescharacteristic
111C2×C42×C139—21no—
112C2×C42×C139—21no—
113C2×C42×C139—21no—
114C2×C42×C139C2311yescharacteristic
115C2×C42×C139C2311yescharacteristic
116#107×C139—22no—
117#107×C139—22no—
118#107×C139—22no—
119#107×C139D414yescomplemented
120#106×C139C2×C414yescomplemented
121#103×C139—22no—
122#103×C139—41no—
123#103×C139C2×C414yescomplemented
124#102×C139—22no—
125#102×C139—41no—
126#102×C139C2×C414yescomplemented
127C22⋊C8×C139—22no—
128#97×C139—22no—
129#97×C139—22no—
130#95×C139—21no—
131#95×C139—21no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139D411yescharacteristic
137#95×C139D411yescharacteristic
138C24×C139—21no—
139C24×C139C2×D411yescharacteristic
140C2×Q8×C139—21no—
141C2×Q8×C139—21no—
142C2×Q8×C139—21no—
143C2×Q8×C139—21no—
144C2×Q8×C139—21no—
145C2×Q8×C139C22×C412yes—
146C2×D4×C139—24no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—42no—
153C2×D4×C139—42no—
154C2×D4×C139C22×C412yes—
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—21no—
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—42no—
167C22×C4×C139—42no—
168C22×C4×C139—42no—
169C22×C4×C139—42no—
170C22×C4×C139—42no—
171C22×C4×C139—42no—
172C22×C4×C139—81no—
173C22×C4×C139—81no—
174C22×C4×C139—81no—
175C22×C4×C139C22×C412yes—
176C22×C4×C139C2×D411yescharacteristic
177C22×C4×C139C2×D411yescharacteristic
178C22×C4×C139C2×D411yescharacteristic
179C22×C4×C139C2×D411yescharacteristic
180C22×C4×C139C2×D411yescharacteristic
181C22×C4×C139#4112yes—
182C22×C4×C139C2411yescharacteristic
183SD16×C139—28no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—28no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
193C2×C8×C139C22×C412yes—
194C2×C8×C139C22×C412yes—
195C2×C8×C139C2×D412yes—
196C2×C8×C139#4112yes—
197C4⋊C4×C139—24no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—21no—
203C4⋊C4×C139—21no—
204C4⋊C4×C139—21no—
205C4⋊C4×C139—21no—
206C4⋊C4×C139—42no—
207C4⋊C4×C139—42no—
208C4⋊C4×C139—42no—
209C4⋊C4×C139—42no—
210C4⋊C4×C139—81no—
211C4⋊C4×C139C22×C412yes—
212C4⋊C4×C139C22×C412yes—
213C4⋊C4×C139C2×D412yes—
214C4⋊C4×C139C2×D412yes—
215C22⋊C4×C139—24no—
216C22⋊C4×C139—22no—
217C22⋊C4×C139—22no—
218C22⋊C4×C139—24no—
219C22⋊C4×C139—42no—
220C22⋊C4×C139—42no—
221C22⋊C4×C139—81no—
222C42×C139—21no—
223C42×C139—21no—
224C42×C139—21no—
225C42×C139—21no—
226C42×C139—42no—
227C42×C139—42no—
228C42×C139—81no—
229C23×C139—21no—
230C23×C139—21no—
231C23×C139—21no—
232C23×C139—21no—
233C23×C139—22no—
234C23×C139—41no—
235C23×C139—41no—
236C23×C139—41no—
237C23×C139—41no—
238C23×C139—41no—
239C23×C139—41no—
240C23×C139C4×D412yes—
241C23×C139AGL(1,ℤ/8)12yes—
242C23×C139#13712yes—
243C23×C139C22×D411yescharacteristic
244Q8×C139—22no—
245Q8×C139—22no—
246Q8×C139—41no—
247Q8×C139—41no—
248D4×C139—22no—
249D4×C139—22no—
250D4×C139—48no—
251D4×C139—41no—
252D4×C139—41no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—22no—
256C2×C4×C139—22no—
257C2×C4×C139—22no—
258C2×C4×C139—22no—
259C2×C4×C139—22no—
260C2×C4×C139—22no—
261C2×C4×C139—22no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—22no—
265C2×C4×C139—22no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—21no—
274C2×C4×C139—21no—
275C2×C4×C139—21no—
276C2×C4×C139—41no—
277C2×C4×C139—41no—
278C2×C4×C139—41no—
279C2×C4×C139—41no—
280C2×C4×C139—41no—
281C2×C4×C139—41no—
282C2×C4×C139—41no—
283C2×C4×C139—41no—
284C2×C4×C139—41no—
285C2×C4×C139—41no—
286C2×C4×C139—41no—
287C2×C4×C139—41no—
288C2×C4×C139—41no—
289C2×C4×C139—41no—
290C2×C4×C139—41no—
291C2×C4×C139—41no—
292C2×C4×C139—84no—
293C2×C4×C139—84no—
294C2×C4×C139—84no—
295C2×C4×C139C4×D412yes—
296C2×C4×C139C23×C411yescharacteristic
297C2×C4×C139C22×D411yescharacteristic
298C2×C4×C139C2×#4111yescharacteristic
299C2×C4×C139C2×#4111yescharacteristic
300C2×C4×C139H(5,𝔽2)11yescharacteristic
301C2×C4×C1392−1+411yescharacteristic
302C8×C139—22no—
303C8×C139—41no—
304C8×C139—41no—
305C8×C139C4×D414yescomplemented
306C22×C139—22no—
307C22×C139—22no—
308C22×C139—22no—
309C22×C139—22no—
310C22×C139—22no—
311C22×C139—22no—
312C22×C139—42no—
313C22×C139—42no—
314C22×C139—42no—
315C22×C139—81no—
316C22×C139—81no—
317C22×C139—81no—
318C22×C139—81no—
319C22×C139#44014yescomplemented
320C22×C139C2×C4×D411yescharacteristic
321C22×C139D4211yescharacteristic
322C22×C139#54711yescharacteristic
323C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C139C2×#13711yescharacteristic
325C22×C139#57611yescharacteristic
326C22×C139#57811yescharacteristic
327C4×C139—22no—
328C4×C139—41no—
329C4×C139—41no—
330C4×C139—42no—
331C4×C139—42no—
332C4×C139—42no—
333C4×C139—41no—
334C4×C139—42no—
335C4×C139—42no—
336C4×C139—41no—
337C4×C139—81no—
338C4×C139—81no—
339C4×C139C2×C4×D411yescharacteristic
340C4×C139#52011yescharacteristic
341C4×C139#54811yescharacteristic
342C4×C139#55311yescharacteristic
343C2×C139—24no—
344C2×C139—82no—
345C2×C139#236111yescharacteristic
346C2×C139C2×#44011yescharacteristic
347C2×C139#295111yescharacteristic
348C2×C139#326411yescharacteristic
349C2×C139#327011yescharacteristic
350C2×C139#334311yescharacteristic
351C2×C139#334611yescharacteristic
352#23032C13911yesmaximal, characteristic, direct product factor, Sylow
353C139#2303211yescharacteristic, direct product factor, Sylow
354C2×#465C2×C13911yescharacteristic
355C2×#440C2×C13911yescharacteristic, complemented
356C22×#107C2×C13911yescharacteristic, complemented
357#2361C2×C13911yescharacteristic
358#2360C2×C13911yescharacteristic, complemented
359#1973C2×C13911yescharacteristic, complemented
360#1944C2×C13911yescharacteristic, complemented
361#1928C2×C13911yescharacteristic, complemented
362#1925C2×C13911yescharacteristic, complemented
363#1874C2×C13911yescharacteristic
364#1872C2×C13911yescharacteristic, complemented
365#1863C2×C13911yescharacteristic, complemented
366#1862C2×C13911yescharacteristic, complemented
367#1776C2×C13911yescharacteristic, complemented
368#1752C2×C13911yescharacteristic, complemented
369C22×SD16C22×C13911yescharacteristic
370C23×C8C22×C13911yescharacteristic
371C2×C22⋊Q8C22×C13911yescharacteristic
372C2×#121C22×C13911yescharacteristic
373C2×C4×Q8C22×C13911yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C22×C13911yescharacteristic
376C22×C4⋊C4C22×C13911yescharacteristic
377C22×C4⋊C4C22×C13911yescharacteristic
378#465C4×C13918yescomplemented
379#440—24no—
380C2×#107—24no—
381C2×#107C22×C13911yescharacteristic
382C2×#107C22×C13911yescharacteristic
383C2×#107C22×C13911yescharacteristic
384C2×#107C22×C13911yescharacteristic
385C2×#106C22×C13911yescharacteristic
386C2×#103C22×C13911yescharacteristic
387C2×#103C22×C13911yescharacteristic
388C2×#103C22×C13911yescharacteristic
389C2×#102C22×C13911yescharacteristic
390C2×#102C22×C13911yescharacteristic
391C2×#102C22×C13911yescharacteristic
392C2×C22⋊C8C22×C13911yescharacteristic
393C2×#97C22×C13911yescharacteristic
394C2×#97C22×C13911yescharacteristic
395#391C22×C13911yescharacteristic
396#390C22×C13911yescharacteristic
397#389—21no—
398#389C22×C13911yescharacteristic
399#389C22×C13911yescharacteristic
400#388—21no—
401#387—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405C4×C4⋊C4C22×C13911yescharacteristic
406C4×C4⋊C4C22×C13911yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4C22×C13911yescharacteristic
409#340C22×C13911yescharacteristic
410#340C22×C13911yescharacteristic
411#340C22×C13911yescharacteristic
412#340C22×C13911yescharacteristic
413#336C22×C13911yescharacteristic
414#336C22×C13911yescharacteristic
415C22×Q8C23×C13911yescharacteristic
416C22×D4—21no—
417C22×D4C23×C13911yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C13911yescharacteristic
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×C4×C13914yescomplemented
425C22×C8—22no—
426C22×C8—22no—
427C22×C8C2×C4×C13914yescomplemented
428C22×C8C23×C13911yescharacteristic
429C22×C8C23×C13911yescharacteristic
430C22×C8C23×C13911yescharacteristic
431C22×C8C23×C13911yescharacteristic
432C22⋊Q8—22no—
433C22⋊Q8C2×C4×C13914yescomplemented
434#121—22no—
435#121C2×C4×C13914yes—
436C4×Q8—22no—
437C4×Q8—41no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—44no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4C23×C13911yescharacteristic
452C2×C4⋊C4C23×C13911yescharacteristic
453C2×C4⋊C4C23×C13911yescharacteristic
454C2×C4⋊C4C23×C13911yescharacteristic
455C2×C4⋊C4C23×C13911yescharacteristic
456C2×C4⋊C4C23×C13911yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C13911yescharacteristic
463C2×C22⋊C4D4×C13911yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C13911yescharacteristic
468C2×C42C23×C13911yescharacteristic
469#107—22no—
470#107—22no—
471#107—22no—
472#107D4×C13914yescomplemented
473#106C2×C4×C13914yescomplemented
474#103—22no—
475#103—41no—
476#103C2×C4×C13914yescomplemented
477#102—22no—
478#102—41no—
479#102C2×C4×C13914yescomplemented
480C22⋊C8—22no—
481#97—22no—
482#97—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C13911yescharacteristic
490#95D4×C13911yescharacteristic
491C24—21no—
492C24C2×D4×C13911yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×C4×C13912yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×C4×C13912yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C22×C4×C13912yes—
529C22×C4C2×D4×C13911yescharacteristic
530C22×C4C2×D4×C13911yescharacteristic
531C22×C4C2×D4×C13911yescharacteristic
532C22×C4C2×D4×C13911yescharacteristic
533C22×C4C2×D4×C13911yescharacteristic
534C22×C4#41×C13912yes—
535C22×C4C24×C13911yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C22×C4×C13912yes—
547C2×C8C22×C4×C13912yes—
548C2×C8C2×D4×C13912yes—
549C2×C8#41×C13912yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—81no—
564C4⋊C4C22×C4×C13912yes—
565C4⋊C4C22×C4×C13912yes—
566C4⋊C4C2×D4×C13912yes—
567C4⋊C4C2×D4×C13912yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—81no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×D4×C13912yes—
594C23AGL(1,ℤ/8)×C13912yes—
595C23#137×C13912yes—
596C23C22×D4×C13911yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C4×D4×C13912yes—
649C2×C4C23×C4×C13911yescharacteristic
650C2×C4C22×D4×C13911yescharacteristic
651C2×C4C2×#41×C13911yescharacteristic
652C2×C4C2×#41×C13911yescharacteristic
653C2×C4H(5,𝔽2)×C13911yescharacteristic
654C2×C42−1+4×C13911yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8C4×D4×C13914yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22#440×C13914yescomplemented
673C22C2×C4×D4×C13911yescharacteristic
674C22D42×C13911yescharacteristic
675C22#547×C13911yescharacteristic
676C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
677C22C2×#137×C13911yescharacteristic
678C22#576×C13911yescharacteristic
679C22#578×C13911yescharacteristic
680C4—22no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4C2×C4×D4×C13911yescharacteristic
693C4#520×C13911yescharacteristic
694C4#548×C13911yescharacteristic
695C4#553×C13911yescharacteristic
696C2—24no—
697C2—82no—
698C2#2361×C13911yescharacteristic
699C2C2×#440×C13911yescharacteristic
700C2#2951×C13911yescharacteristic
701C2#3264×C13911yescharacteristic
702C2#3270×C13911yescharacteristic
703C2#3343×C13911yescharacteristic
704C2#3346×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#121×C139C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C139C2semidirect
3. C22×#107×C139C2semidirect
5. #2360×C139C2semidirect
6. #1973×C139C2semidirect
7. #1944×C139C2semidirect
8. #1928×C139C2semidirect
9. #1925×C139C2semidirect
11. #1872×C139C2semidirect
12. #1863×C139C2semidirect
13. #1862×C139C2semidirect
14. #1776×C139C2semidirect
15. #1752×C139C2semidirect
25. #465×C139C4semidirect
71. C2×SD16×C139C2×C4semidirect
74. C22×C8×C139C2×C4semidirect
80. C22⋊Q8×C139C2×C4semidirect
119. #107×C139D4semidirect
120. #106×C139C2×C4semidirect
123. #103×C139C2×C4semidirect
126. #102×C139C2×C4semidirect
305. C8×C139C4×D4semidirect
319. C22×C139#440semidirect
352. #23032C139direct (N × H)
353. C139#23032direct (N × H)
355. C2×#440C2×C139semidirect
356. C22×#107C2×C139semidirect
358. #2360C2×C139semidirect
359. #1973C2×C139semidirect
360. #1944C2×C139semidirect
361. #1928C2×C139semidirect
362. #1925C2×C139semidirect
364. #1872C2×C139semidirect
365. #1863C2×C139semidirect
366. #1862C2×C139semidirect
367. #1776C2×C139semidirect
368. #1752C2×C139semidirect
378. #465C4×C139semidirect
424. C2×SD16C2×C4×C139semidirect
427. C22×C8C2×C4×C139semidirect
433. C22⋊Q8C2×C4×C139semidirect
472. #107D4×C139semidirect
473. #106C2×C4×C139semidirect
476. #103C2×C4×C139semidirect
479. #102C2×C4×C139semidirect
658. C8C4×D4×C139semidirect
672. C22#440×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1392
C2×#440×C1392
C22×#107×C1392
#2361×C1392
#2360×C1392
#1973×C1392
#1944×C1392
#1928×C1392
#1925×C1392
#1874×C1392
#1872×C1392
#1863×C1392
#1862×C1392
#1776×C1392
#1752×C1392
#23032139