Finite Group Databasebeta

← C139×#24474 #48019070

Subgroups — C139×#24474 #48019070

Order 35584.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C139C211yesmaximal, characteristic
2#3069×C139C211yesmaximal, characteristic, complemented
3#3039×C139C211yesmaximal, characteristic, complemented
4#3022×C139C211yesmaximal, characteristic, complemented
5C2×#456×C139C211yesmaximal, characteristic, complemented
6#2901×C139C211yesmaximal, characteristic, complemented
7#2050×C139C211yesmaximal, characteristic, complemented
8#2049×C139C211yesmaximal, characteristic, complemented
9#2009×C139C211yesmaximal, characteristic, complemented
10#2005×C139C211yesmaximal, characteristic, complemented
11#1906×C139C211yesmaximal, characteristic, complemented
12#1902×C139C211yesmaximal, characteristic, complemented
13#1902×C139C211yesmaximal, characteristic, complemented
14#1861×C139C211yesmaximal, characteristic, complemented
15#1796×C139C211yesmaximal, characteristic, complemented
16#585×C139C2211yescharacteristic
17C2×2−1+4×C139C2211yescharacteristic
18#578×C139—22no—
19#578×C139—22no—
20#577×C139—22no—
21#577×C139—22no—
22#575×C139—22no—
23#575×C139C2211yescharacteristic
24#575×C139C2211yescharacteristic
25C2×#137×C139—22no—
26C2×#137×C139C2211yescharacteristic
27C2×#137×C139C2211yescharacteristic
28C2×#137×C139C2211yescharacteristic
29C2×#137×C139C2211yescharacteristic
30C2×#137×C139C2211yescharacteristic, complemented
31#568×C139C2211yescharacteristic
32#568×C139C2211yescharacteristic
33#536×C139C2211yescharacteristic
34C2×C4⋊Q8×C139C2211yescharacteristic, complemented
35C4×#41×C139C2211yescharacteristic
36#473×C139—22no—
37#471×C139—22no—
38#462×C139—22no—
39#461×C139—22no—
40#456×C139—22no—
41#456×C139—22no—
42#456×C139—22no—
43#455×C139—22no—
44#430×C139C2211yescharacteristic, complemented
45#423×C139C2211yescharacteristic, complemented
46#421×C139—22no—
47#421×C139C2211yescharacteristic
48#421×C139C2211yescharacteristic
49#421×C139C2211yescharacteristic
50#421×C139C2211yescharacteristic
51C2×#104×C139—22no—
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic
54C2×#104×C139C2211yescharacteristic, complemented
55#419×C139C2211yescharacteristic, complemented
56#419×C139C2211yescharacteristic, complemented
57#419×C139C2211yescharacteristic, complemented
58#413×C139C2211yescharacteristic
59#413×C139C2211yescharacteristic, complemented
60C2×#101×C139C2211yescharacteristic, complemented
61C2×#101×C139C2211yescharacteristic, complemented
62#410×C139C2211yescharacteristic, complemented
63#344×C139C2211yescharacteristic, complemented
64#344×C139C2211yescharacteristic, complemented
65#339×C139C2211yescharacteristic, complemented
66#338×C139C2211yescharacteristic, complemented
672−1+4×C139—22no—
682−1+4×C139—22no—
692−1+4×C139—21no—
702−1+4×C139—21no—
712−1+4×C139—22no—
722−1+4×C139—41no—
732−1+4×C139D412yes—
74H(5,𝔽2)×C139—21no—
75H(5,𝔽2)×C139—21no—
76H(5,𝔽2)×C139—41no—
77H(5,𝔽2)×C139D412yes—
78C2×#41×C139—22no—
79C2×#41×C139—22no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—41no—
83C2×#41×C139—41no—
84C2×#41×C139C2311yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C2×#41×C139C2311yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C22×Q8×C139—21no—
89C22×Q8×C139—21no—
90C22×Q8×C139C2311yescharacteristic
91C22×Q8×C139C2311yescharacteristic
92#137×C139—24no—
93#137×C139—24no—
94#137×C139—24no—
95#137×C139—22no—
96#137×C139—22no—
97#137×C139—21no—
98#137×C139—22no—
99#137×C139—21no—
100#137×C139—21no—
101#137×C139—22no—
102#137×C139—22no—
103#137×C139—22no—
104#137×C139—22no—
105#137×C139—22no—
106#137×C139—22no—
107#137×C139—41no—
108#137×C139D412yes—
109AGL(1,ℤ/8)×C139—24no—
110AGL(1,ℤ/8)×C139—21no—
111AGL(1,ℤ/8)×C139—21no—
112AGL(1,ℤ/8)×C139—21no—
113AGL(1,ℤ/8)×C139D412yes—
114#135×C139—24no—
115#135×C139—24no—
116#135×C139—22no—
117#135×C139—22no—
118C2×Q16×C139—24no—
119C2×Q16×C139—21no—
120C2×Q16×C139—21no—
121C2×Q16×C139—21no—
122C2×Q16×C139—21no—
123C2×Q16×C139D412yes—
124C2×SD16×C139—24no—
125C2×SD16×C139—21no—
126C2×SD16×C139—21no—
127C2×SD16×C139—21no—
128C2×SD16×C139—21no—
129C2×SD16×C139D412yes—
130#131×C139—22no—
131#131×C139—22no—
132#131×C139—22no—
133#131×C139—41no—
134C2×M16×C139—22no—
135C2×M16×C139—22no—
136C2×M16×C139C2311yescharacteristic
137C2×M16×C139C2311yescharacteristic
138C2×M16×C139C2311yescharacteristic
139C2×M16×C139C2311yescharacteristic
140C2×M16×C139C2311yescharacteristic
141C2×M16×C139C2311yescharacteristic
142C4⋊Q8×C139—21no—
143C4⋊Q8×C139—22no—
144C4⋊Q8×C139—21no—
145C4⋊Q8×C139—21no—
146#124×C139—21no—
147#123×C139—41no—
148C22⋊Q8×C139—41no—
149C4×Q8×C139—21no—
150C4×D4×C139—21no—
151C4×D4×C139—41no—
152#117×C139—21no—
153#117×C139C2311yescharacteristic
154#117×C139C2311yescharacteristic
155C2×C4⋊C4×C139—41no—
156C2×C42×C139—21no—
157C2×C42×C139C2311yescharacteristic
158#108×C139—22no—
159C4⋊C8×C139—22no—
160#104×C139—22no—
161#104×C139—22no—
162#104×C139—22no—
163#104×C139—22no—
164#104×C139—21no—
165#104×C139—21no—
166#104×C139—21no—
167#104×C139—21no—
168#104×C139D412yes—
169#104×C139D412yes—
170#103×C139—22no—
171#103×C139—22no—
172#103×C139—41no—
173#101×C139—21no—
174#101×C139—21no—
175#101×C139—22no—
176#101×C139—22no—
177#100×C139—21no—
178#100×C139—21no—
179#99×C139—41no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—21no—
183#41×C139—21no—
184#41×C139—24no—
185#41×C139—22no—
186#41×C139—22no—
187#41×C139—22no—
188#41×C139—22no—
189#41×C139—21no—
190#41×C139—21no—
191#41×C139—21no—
192#41×C139—21no—
193#41×C139—21no—
194#41×C139—21no—
195#41×C139—21no—
196#41×C139—21no—
197#41×C139—42no—
198#41×C139—42no—
199#41×C139—42no—
200#41×C139—42no—
201#41×C139—42no—
202#41×C139—44no—
203#41×C139—42no—
204#41×C139—41no—
205#41×C139—41no—
206#41×C139—44no—
207#41×C139—42no—
208#41×C139C2×D412yes—
209#41×C139C2×D412yes—
210#41×C139C2×D412yes—
211#41×C139C2×D412yes—
212C2×Q8×C139—21no—
213C2×Q8×C139—24no—
214C2×Q8×C139—22no—
215C2×Q8×C139—22no—
216C2×Q8×C139—21no—
217C2×Q8×C139—21no—
218C2×Q8×C139—21no—
219C2×Q8×C139—21no—
220C2×Q8×C139—21no—
221C2×Q8×C139—21no—
222C2×Q8×C139—21no—
223C2×Q8×C139—21no—
224C2×Q8×C139—21no—
225C2×Q8×C139—21no—
226C2×Q8×C139—41no—
227C2×Q8×C139—42no—
228C2×Q8×C139—42no—
229C2×Q8×C139—41no—
230C2×Q8×C139—42no—
231C2×Q8×C139C2×D411yescharacteristic
232C2×Q8×C139C2×D411yescharacteristic
233C2×Q8×C139C2×D412yes—
234C2×Q8×C139C2×D411yescharacteristic
235C2×Q8×C139#4111yescharacteristic
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—22no—
239C2×D4×C139—22no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—42no—
243C2×D4×C139—41no—
244C2×D4×C139—42no—
245C2×D4×C139—42no—
246C2×D4×C139—41no—
247C2×D4×C139C2×D411yescharacteristic
248C2×D4×C139C2×D411yescharacteristic
249C2×D4×C139C2×D411yescharacteristic
250C2×D4×C139#4111yescharacteristic
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—42no—
259C22×C4×C139—41no—
260C22×C4×C139—41no—
261C22×C4×C139—41no—
262C22×C4×C139C2411yescharacteristic
263Q16×C139—24no—
264Q16×C139—22no—
265Q16×C139—22no—
266Q16×C139—24no—
267Q16×C139—42no—
268Q16×C139—42no—
269Q16×C139—42no—
270SD16×C139—24no—
271SD16×C139—22no—
272SD16×C139—22no—
273SD16×C139—22no—
274SD16×C139—22no—
275SD16×C139—24no—
276SD16×C139—42no—
277SD16×C139—42no—
278SD16×C139—42no—
279D8×C139—22no—
280D8×C139—22no—
281M16×C139—24no—
282M16×C139—21no—
283M16×C139—21no—
284M16×C139—21no—
285M16×C139—21no—
286M16×C139—21no—
287M16×C139—21no—
288M16×C139—21no—
289M16×C139—21no—
290M16×C139—21no—
291M16×C139—21no—
292M16×C139—42no—
293M16×C139C2×D412yes—
294M16×C139C2×D412yes—
295C2×C8×C139—24no—
296C2×C8×C139—21no—
297C2×C8×C139—21no—
298C2×C8×C139—21no—
299C2×C8×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139—42no—
302C2×C8×C139C2×D412yes—
303C4⋊C4×C139—21no—
304C4⋊C4×C139—21no—
305C4⋊C4×C139—42no—
306C4⋊C4×C139—42no—
307C4⋊C4×C139—41no—
308C4⋊C4×C139—42no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—41no—
312C22⋊C4×C139—42no—
313C42×C139—21no—
314C42×C139—21no—
315C42×C139—21no—
316C42×C139—41no—
317C42×C139C2×D411yescharacteristic
318C42×C139C2×D411yescharacteristic
319C23×C139—21no—
320C23×C139—21no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—42no—
324C23×C139H(5,𝔽2)11yescharacteristic
325Q8×C139—21no—
326Q8×C139—21no—
327Q8×C139—21no—
328Q8×C139—22no—
329Q8×C139—21no—
330Q8×C139—21no—
331Q8×C139—21no—
332Q8×C139—22no—
333Q8×C139—42no—
334Q8×C139—44no—
335Q8×C139—41no—
336Q8×C139—41no—
337Q8×C139—41no—
338Q8×C139—41no—
339Q8×C139—41no—
340Q8×C139—41no—
341Q8×C139#12012yes—
342Q8×C139#12112yes—
343D4×C139—22no—
344D4×C139—22no—
345D4×C139—22no—
346D4×C139—22no—
347D4×C139—21no—
348D4×C139—21no—
349D4×C139—21no—
350D4×C139—21no—
351D4×C139—21no—
352D4×C139—21no—
353D4×C139—42no—
354D4×C139—42no—
355D4×C139—42no—
356D4×C139—44no—
357D4×C139—41no—
358D4×C139—41no—
359D4×C139—41no—
360D4×C139—41no—
361D4×C139#12012yes—
362D4×C139#12112yes—
363C2×C4×C139—21no—
364C2×C4×C139—21no—
365C2×C4×C139—21no—
366C2×C4×C139—22no—
367C2×C4×C139—22no—
368C2×C4×C139—22no—
369C2×C4×C139—22no—
370C2×C4×C139—21no—
371C2×C4×C139—21no—
372C2×C4×C139—22no—
373C2×C4×C139—21no—
374C2×C4×C139—42no—
375C2×C4×C139—42no—
376C2×C4×C139—42no—
377C2×C4×C139—42no—
378C2×C4×C139—44no—
379C2×C4×C139—44no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
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—82no—
392C2×C4×C139C22×D411yescharacteristic
393C2×C4×C139C22×D411yescharacteristic
394C2×C4×C139C22×D411yescharacteristic
395C2×C4×C139C22×D411yescharacteristic
396C2×C4×C139C2×#4111yescharacteristic
397C2×C4×C139H(5,𝔽2)11yescharacteristic
398C8×C139—22no—
399C8×C139—22no—
400C8×C139—22no—
401C8×C139—41no—
402C8×C139—41no—
403C8×C139—41no—
404C22×C139—22no—
405C22×C139—22no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—41no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139—162no—
414C22×C139#53411yescharacteristic
415C22×C139D4211yescharacteristic
416C22×C139#54611yescharacteristic
417C4×C139—22no—
418C4×C139—22no—
419C4×C139—22no—
420C4×C139—41no—
421C4×C139—41no—
422C4×C139—42no—
423C4×C139—41no—
424C4×C139—81no—
425C4×C139—81no—
426C4×C139—81no—
427C4×C139C2×#12011yescharacteristic
428C4×C139C2×#12111yescharacteristic
429C4×C139D4211yescharacteristic
430C4×C139#54611yescharacteristic
431C2×C139—21no—
432C2×C139—21no—
433C2×C139—21no—
434C2×C139—42no—
435C2×C139—42no—
436C2×C139—81no—
437C2×C139—81no—
438C2×C139#241011yescharacteristic
439#24474C13911yesmaximal, characteristic, direct product factor, Sylow
440C139#2447411yescharacteristic, direct product factor, Sylow
441#3586C2×C13911yescharacteristic
442#3069C2×C13911yescharacteristic, complemented
443#3039C2×C13911yescharacteristic, complemented
444#3022C2×C13911yescharacteristic, complemented
445C2×#456C2×C13911yescharacteristic, complemented
446#2901C2×C13911yescharacteristic, complemented
447#2050C2×C13911yescharacteristic, complemented
448#2049C2×C13911yescharacteristic, complemented
449#2009C2×C13911yescharacteristic, complemented
450#2005C2×C13911yescharacteristic, complemented
451#1906C2×C13911yescharacteristic, complemented
452#1902C2×C13911yescharacteristic, complemented
453#1902C2×C13911yescharacteristic, complemented
454#1861C2×C13911yescharacteristic, complemented
455#1796C2×C13911yescharacteristic, complemented
456#585C22×C13911yescharacteristic
457C2×2−1+4C22×C13911yescharacteristic
458#578—22no—
459#578—22no—
460#577—22no—
461#577—22no—
462#575—22no—
463#575C22×C13911yescharacteristic
464#575C22×C13911yescharacteristic
465C2×#137—22no—
466C2×#137C22×C13911yescharacteristic
467C2×#137C22×C13911yescharacteristic
468C2×#137C22×C13911yescharacteristic
469C2×#137C22×C13911yescharacteristic
470C2×#137C22×C13911yescharacteristic, complemented
471#568C22×C13911yescharacteristic
472#568C22×C13911yescharacteristic
473#536C22×C13911yescharacteristic
474C2×C4⋊Q8C22×C13911yescharacteristic, complemented
475C4×#41C22×C13911yescharacteristic
476#473—22no—
477#471—22no—
478#462—22no—
479#461—22no—
480#456—22no—
481#456—22no—
482#456—22no—
483#455—22no—
484#430C22×C13911yescharacteristic, complemented
485#423C22×C13911yescharacteristic, complemented
486#421—22no—
487#421C22×C13911yescharacteristic
488#421C22×C13911yescharacteristic
489#421C22×C13911yescharacteristic
490#421C22×C13911yescharacteristic
491C2×#104—22no—
492C2×#104C22×C13911yescharacteristic
493C2×#104C22×C13911yescharacteristic
494C2×#104C22×C13911yescharacteristic, complemented
495#419C22×C13911yescharacteristic, complemented
496#419C22×C13911yescharacteristic, complemented
497#419C22×C13911yescharacteristic, complemented
498#413C22×C13911yescharacteristic
499#413C22×C13911yescharacteristic, complemented
500C2×#101C22×C13911yescharacteristic, complemented
501C2×#101C22×C13911yescharacteristic, complemented
502#410C22×C13911yescharacteristic, complemented
503#344C22×C13911yescharacteristic, complemented
504#344C22×C13911yescharacteristic, complemented
505#339C22×C13911yescharacteristic, complemented
506#338C22×C13911yescharacteristic, complemented
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C13912yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C13912yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C13911yescharacteristic
525C2×#41C23×C13911yescharacteristic
526C2×#41C23×C13911yescharacteristic
527C2×#41C23×C13911yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C13911yescharacteristic
531C22×Q8C23×C13911yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C13912yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C13912yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C13912yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C13912yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C13911yescharacteristic
577C2×M16C23×C13911yescharacteristic
578C2×M16C23×C13911yescharacteristic
579C2×M16C23×C13911yescharacteristic
580C2×M16C23×C13911yescharacteristic
581C2×M16C23×C13911yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C13911yescharacteristic
594#117C23×C13911yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C13911yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C13912yes—
609#104D4×C13912yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C13912yes—
649#41C2×D4×C13912yes—
650#41C2×D4×C13912yes—
651#41C2×D4×C13912yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C13911yescharacteristic
672C2×Q8C2×D4×C13911yescharacteristic
673C2×Q8C2×D4×C13912yes—
674C2×Q8C2×D4×C13911yescharacteristic
675C2×Q8#41×C13911yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C13911yescharacteristic
688C2×D4C2×D4×C13911yescharacteristic
689C2×D4C2×D4×C13911yescharacteristic
690C2×D4#41×C13911yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C13911yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C13912yes—
734M16C2×D4×C13912yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C13912yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C13911yescharacteristic
758C42C2×D4×C13911yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C13911yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C13912yes—
782Q8#121×C13912yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C13912yes—
802D4#121×C13912yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C13911yescharacteristic
833C2×C4C22×D4×C13911yescharacteristic
834C2×C4C22×D4×C13911yescharacteristic
835C2×C4C22×D4×C13911yescharacteristic
836C2×C4C2×#41×C13911yescharacteristic
837C2×C4H(5,𝔽2)×C13911yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22#534×C13911yescharacteristic
855C22D42×C13911yescharacteristic
856C22#546×C13911yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C13911yescharacteristic
868C4C2×#121×C13911yescharacteristic
869C4D42×C13911yescharacteristic
870C4#546×C13911yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2#2410×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2410
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3586×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3069×C139C2semidirect
3. #3039×C139C2semidirect
4. #3022×C139C2semidirect
5. C2×#456×C139C2semidirect
6. #2901×C139C2semidirect
7. #2050×C139C2semidirect
8. #2049×C139C2semidirect
9. #2009×C139C2semidirect
10. #2005×C139C2semidirect
11. #1906×C139C2semidirect
12. #1902×C139C2semidirect
13. #1902×C139C2semidirect
14. #1861×C139C2semidirect
15. #1796×C139C2semidirect
30. C2×#137×C139C22semidirect
34. C2×C4⋊Q8×C139C22semidirect
44. #430×C139C22semidirect
45. #423×C139C22semidirect
54. C2×#104×C139C22semidirect
55. #419×C139C22semidirect
56. #419×C139C22semidirect
57. #419×C139C22semidirect
59. #413×C139C22semidirect
60. C2×#101×C139C22semidirect
61. C2×#101×C139C22semidirect
62. #410×C139C22semidirect
63. #344×C139C22semidirect
64. #344×C139C22semidirect
65. #339×C139C22semidirect
66. #338×C139C22semidirect
439. #24474C139direct (N × H)
440. C139#24474direct (N × H)
442. #3069C2×C139semidirect
443. #3039C2×C139semidirect
444. #3022C2×C139semidirect
445. C2×#456C2×C139semidirect
446. #2901C2×C139semidirect
447. #2050C2×C139semidirect
448. #2049C2×C139semidirect
449. #2009C2×C139semidirect
450. #2005C2×C139semidirect
451. #1906C2×C139semidirect
452. #1902C2×C139semidirect
453. #1902C2×C139semidirect
454. #1861C2×C139semidirect
455. #1796C2×C139semidirect
470. C2×#137C22×C139semidirect
474. C2×C4⋊Q8C22×C139semidirect
484. #430C22×C139semidirect
485. #423C22×C139semidirect
494. C2×#104C22×C139semidirect
495. #419C22×C139semidirect
496. #419C22×C139semidirect
497. #419C22×C139semidirect
499. #413C22×C139semidirect
500. C2×#101C22×C139semidirect
501. C2×#101C22×C139semidirect
502. #410C22×C139semidirect
503. #344C22×C139semidirect
504. #344C22×C139semidirect
505. #339C22×C139semidirect
506. #338C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3586×C1392
#3069×C1392
#3039×C1392
#3022×C1392
C2×#456×C1392
#2901×C1392
#2050×C1392
#2049×C1392
#2009×C1392
#2005×C1392
#1906×C1392
#1902×C1392
#1861×C1392
#1796×C1392
#24474139