Finite Group Databasebeta

← C139×#24031 #48018627

Subgroups — C139×#24031 #48018627

Order 35584.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C139C211yesmaximal, characteristic
2#3093×C139C211yesmaximal, characteristic, complemented
3#2896×C139C211yesmaximal, characteristic, complemented
4#2500×C139C211yesmaximal, characteristic, complemented
5#2040×C139C211yesmaximal, characteristic, complemented
6#2039×C139C211yesmaximal, characteristic, complemented
7#2037×C139C211yesmaximal, characteristic, complemented
8#2037×C139C211yesmaximal, characteristic, complemented
9#1900×C139C211yesmaximal, characteristic, complemented
10#1871×C139C211yesmaximal, characteristic, complemented
11#1860×C139C211yesmaximal, characteristic, complemented
12#1859×C139C211yesmaximal, characteristic, complemented
13#1792×C139C211yesmaximal, characteristic, complemented
14#1792×C139C211yesmaximal, characteristic, complemented
15#1789×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic, complemented
19#550×C139—21no—
20#548×C139—21no—
21#546×C139—21no—
22#546×C139—22no—
23D42×C139—22no—
24D42×C139—21no—
25#537×C139—21no—
26#537×C139C2211yescharacteristic
27#535×C139—21no—
28#535×C139C2211yescharacteristic
29#525×C139—21no—
30#525×C139C2211yescharacteristic
31C2×#121×C139—21no—
32C2×#121×C139C2211yescharacteristic
33#520×C139C2211yescharacteristic
34C2×#117×C139C2211yescharacteristic, complemented
35#485×C139—21no—
36#485×C139—21no—
37#482×C139—21no—
38#482×C139—21no—
39#428×C139C2211yescharacteristic, complemented
40#428×C139C2211yescharacteristic, complemented
41C2×#104×C139C2211yescharacteristic
42C2×#104×C139C2211yescharacteristic
43C2×#104×C139C2211yescharacteristic, complemented
44C2×#104×C139C2211yescharacteristic, complemented
45C2×#104×C139C2211yescharacteristic, complemented
46C2×#104×C139C2211yescharacteristic, complemented
47#419×C139—21no—
48#418×C139—21no—
49#417×C139C2211yescharacteristic
50#417×C139C2211yescharacteristic
51#417×C139C2211yescharacteristic, complemented
52#417×C139C2211yescharacteristic, complemented
53#417×C139C2211yescharacteristic, complemented
54#417×C139C2211yescharacteristic, complemented
55#416×C139—21no—
56#416×C139—21no—
57C2×#100×C139C2211yescharacteristic, complemented
58C2×#100×C139C2211yescharacteristic, complemented
59#407×C139C2211yescharacteristic, complemented
60#394×C139—22no—
61#390×C139C2211yescharacteristic, complemented
62#390×C139C2211yescharacteristic, complemented
63#388×C139—22no—
64#384×C139C2211yescharacteristic, complemented
65#382×C139C2211yescharacteristic, complemented
66C4×C22⋊C4×C139C2211yescharacteristic, complemented
67#343×C139C2211yescharacteristic, complemented
68#343×C139C2211yescharacteristic, complemented
69#339×C139C2211yescharacteristic, complemented
70#339×C139C2211yescharacteristic, complemented
71H(5,𝔽2)×C139—22no—
72H(5,𝔽2)×C139—22no—
73H(5,𝔽2)×C139—41no—
74H(5,𝔽2)×C139—41no—
75C2×#41×C139—21no—
76C2×#41×C139—21no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—22no—
80C2×#41×C139—22no—
81C2×#41×C139—41no—
82C2×#41×C139—41no—
83C2×#41×C139D411yescharacteristic
84C2×#41×C139D411yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C2×#41×C139C2311yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C22×Q8×C139D411yescharacteristic
89C22×D4×C139—21no—
90C22×D4×C139—22no—
91C22×D4×C139—22no—
92C22×D4×C139—21no—
93C22×D4×C139—21no—
94C22×D4×C139D411yescharacteristic
95C22×D4×C139D412yes—
96C22×D4×C139C2311yescharacteristic
97C23×C4×C139—21no—
98C23×C4×C139C2311yescharacteristic
99C2×M16×C139—21no—
100C2×M16×C139—41no—
101C2×M16×C139—41no—
102C2×M16×C139C2311yescharacteristic
103C2×M16×C139C2311yescharacteristic
104C2×M16×C139C2311yescharacteristic
105C2×M16×C139C2311yescharacteristic
106C22×C8×C139—21no—
107#127×C139—22no—
108#127×C139—21no—
109#124×C139—22no—
110#124×C139—21no—
111#123×C139—22no—
112#123×C139—21no—
113C22⋊Q8×C139—22no—
114C22⋊Q8×C139—21no—
115C22⋊Q8×C139—21no—
116C22⋊Q8×C139D411yescharacteristic
117C22⋊Q8×C139D411yescharacteristic
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139—21no—
124#121×C139—21no—
125#121×C139—21no—
126#121×C139—21no—
127#121×C139—21no—
128#121×C139—21no—
129#121×C139—22no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139D411yescharacteristic
133#121×C139D411yescharacteristic
134#120×C139—22no—
135#120×C139—22no—
136#120×C139—22no—
137#120×C139—21no—
138#120×C139—22no—
139C4×Q8×C139—21no—
140C4×D4×C139—22no—
141C4×D4×C139—22no—
142C4×D4×C139—21no—
143C4×D4×C139—22no—
144C4×D4×C139—21no—
145C4×D4×C139—21no—
146#117×C139—21no—
147#117×C139—21no—
148#117×C139—21no—
149#117×C139—21no—
150#117×C139—21no—
151#117×C139C2311yescharacteristic
152C2×C4⋊C4×C139—21no—
153C2×C4⋊C4×C139—22no—
154C2×C4⋊C4×C139C2311yescharacteristic
155C2×C4⋊C4×C139C2311yescharacteristic
156C2×C4⋊C4×C139C2311yescharacteristic
157C2×C22⋊C4×C139—22no—
158C2×C22⋊C4×C139—21no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—22no—
161C2×C22⋊C4×C139—22no—
162C2×C22⋊C4×C139D412yes—
163C2×C42×C139—21no—
164C2×C42×C139C2311yescharacteristic
165C2×C42×C139C2311yescharacteristic
166#107×C139—21no—
167#107×C139—21no—
168#106×C139—21no—
169#106×C139—21no—
170#104×C139—22no—
171#104×C139—22no—
172#104×C139—41no—
173#104×C139—41no—
174#104×C139—41no—
175#104×C139—41no—
176#103×C139—21no—
177#103×C139—21no—
178#103×C139—21no—
179#103×C139—21no—
180#103×C139—21no—
181#103×C139—21no—
182#102×C139—21no—
183#102×C139—21no—
184#102×C139—21no—
185#102×C139—21no—
186#102×C139—21no—
187#102×C139—21no—
188#100×C139—41no—
189#100×C139—41no—
190C22⋊C8×C139—21no—
191C22⋊C8×C139—21no—
192#95×C139—21no—
193#95×C139—22no—
194C24×C139—22no—
195C24×C139—21no—
196C24×C139C2×D412yes—
197C24×C139C2×D411yescharacteristic
198#41×C139—21no—
199#41×C139—21no—
200#41×C139—22no—
201#41×C139—22no—
202#41×C139—21no—
203#41×C139—21no—
204#41×C139—21no—
205#41×C139—21no—
206#41×C139—21no—
207#41×C139—21no—
208#41×C139—21no—
209#41×C139—21no—
210#41×C139—42no—
211#41×C139—42no—
212#41×C139—41no—
213#41×C139—41no—
214#41×C139—42no—
215#41×C139—42no—
216#41×C139—42no—
217#41×C139—42no—
218#41×C139—42no—
219#41×C139—42no—
220#41×C139#4112yes—
221#41×C139#4112yes—
222C2×Q8×C139—21no—
223C2×Q8×C139—22no—
224C2×Q8×C139—41no—
225C2×Q8×C139C2×D411yescharacteristic
226C2×Q8×C139C2×D411yescharacteristic
227C2×Q8×C139C2×D411yescharacteristic
228C2×D4×C139—21no—
229C2×D4×C139—22no—
230C2×D4×C139—22no—
231C2×D4×C139—22no—
232C2×D4×C139—22no—
233C2×D4×C139—21no—
234C2×D4×C139—21no—
235C2×D4×C139—21no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—22no—
239C2×D4×C139—22no—
240C2×D4×C139—22no—
241C2×D4×C139—21no—
242C2×D4×C139—22no—
243C2×D4×C139—21no—
244C2×D4×C139—21no—
245C2×D4×C139—21no—
246C2×D4×C139—21no—
247C2×D4×C139—21no—
248C2×D4×C139—21no—
249C2×D4×C139—21no—
250C2×D4×C139—41no—
251C2×D4×C139—42no—
252C2×D4×C139—42no—
253C2×D4×C139—42no—
254C2×D4×C139—42no—
255C2×D4×C139—44no—
256C2×D4×C139—44no—
257C2×D4×C139—42no—
258C2×D4×C139—42no—
259C2×D4×C139—82no—
260C2×D4×C139—84no—
261C2×D4×C139C2×D411yescharacteristic
262C2×D4×C139C2×D411yescharacteristic
263C2×D4×C139C2×D411yescharacteristic
264C22×C4×C139—21no—
265C22×C4×C139—21no—
266C22×C4×C139—21no—
267C22×C4×C139—21no—
268C22×C4×C139—21no—
269C22×C4×C139—22no—
270C22×C4×C139—21no—
271C22×C4×C139—21no—
272C22×C4×C139—22no—
273C22×C4×C139—21no—
274C22×C4×C139—21no—
275C22×C4×C139—21no—
276C22×C4×C139—21no—
277C22×C4×C139—21no—
278C22×C4×C139—21no—
279C22×C4×C139—21no—
280C22×C4×C139—42no—
281C22×C4×C139—42no—
282C22×C4×C139C2×D411yescharacteristic
283C22×C4×C139C2×D411yescharacteristic
284C22×C4×C139C2×D411yescharacteristic
285C22×C4×C139C2×D411yescharacteristic
286C22×C4×C139C2×D411yescharacteristic
287C22×C4×C139C2×D412yes—
288C22×C4×C139C2411yescharacteristic
289M16×C139—21no—
290M16×C139—21no—
291M16×C139—21no—
292M16×C139—21no—
293M16×C139—21no—
294M16×C139—21no—
295M16×C139—21no—
296M16×C139—21no—
297M16×C139—42no—
298C2×C8×C139—21no—
299C2×C8×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139—21no—
302C2×C8×C139—42no—
303C4⋊C4×C139—22no—
304C4⋊C4×C139—22no—
305C4⋊C4×C139—21no—
306C4⋊C4×C139—21no—
307C4⋊C4×C139—21no—
308C4⋊C4×C139—21no—
309C4⋊C4×C139—21no—
310C4⋊C4×C139—21no—
311C4⋊C4×C139—21no—
312C4⋊C4×C139—21no—
313C4⋊C4×C139—82no—
314C4⋊C4×C139C2×D411yescharacteristic
315C4⋊C4×C139C2×D411yescharacteristic
316C22⋊C4×C139—22no—
317C22⋊C4×C139—22no—
318C22⋊C4×C139—22no—
319C22⋊C4×C139—22no—
320C22⋊C4×C139—22no—
321C22⋊C4×C139—21no—
322C22⋊C4×C139—21no—
323C22⋊C4×C139—21no—
324C22⋊C4×C139—21no—
325C22⋊C4×C139—22no—
326C22⋊C4×C139—22no—
327C22⋊C4×C139—21no—
328C22⋊C4×C139—42no—
329C22⋊C4×C139—44no—
330C22⋊C4×C139—41no—
331C22⋊C4×C139—41no—
332C22⋊C4×C139—82no—
333C42×C139—22no—
334C42×C139—21no—
335C42×C139—21no—
336C42×C139—21no—
337C42×C139—21no—
338C42×C139—21no—
339C42×C139—41no—
340C42×C139—41no—
341C23×C139—21no—
342C23×C139—21no—
343C23×C139—21no—
344C23×C139—22no—
345C23×C139—21no—
346C23×C139—21no—
347C23×C139—22no—
348C23×C139—22no—
349C23×C139—41no—
350C23×C139—41no—
351C23×C139—42no—
352C23×C139—42no—
353C23×C139—44no—
354C23×C139—42no—
355C23×C139—42no—
356C23×C139—81no—
357C23×C139—82no—
358C23×C139—82no—
359C23×C139#12011yescharacteristic
360C23×C139#12011yescharacteristic
361C23×C139C22×D411yescharacteristic
362Q8×C139—21no—
363Q8×C139—21no—
364Q8×C139—21no—
365Q8×C139—21no—
366Q8×C139—21no—
367Q8×C139—42no—
368Q8×C139#12312yes—
369D4×C139—22no—
370D4×C139—22no—
371D4×C139—21no—
372D4×C139—21no—
373D4×C139—21no—
374D4×C139—21no—
375D4×C139—21no—
376D4×C139—42no—
377D4×C139—42no—
378D4×C139—44no—
379D4×C139—42no—
380D4×C139—44no—
381D4×C139—44no—
382D4×C139—42no—
383D4×C139—41no—
384D4×C139—41no—
385D4×C139—41no—
386D4×C139—41no—
387D4×C139—41no—
388D4×C139—41no—
389D4×C139—41no—
390D4×C139—41no—
391D4×C139—81no—
392D4×C139—82no—
393D4×C139—82no—
394D4×C139—82no—
395D4×C139—82no—
396D4×C139#12312yes—
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—21no—
402C2×C4×C139—21no—
403C2×C4×C139—21no—
404C2×C4×C139—21no—
405C2×C4×C139—21no—
406C2×C4×C139—21no—
407C2×C4×C139—21no—
408C2×C4×C139—22no—
409C2×C4×C139—22no—
410C2×C4×C139—22no—
411C2×C4×C139—21no—
412C2×C4×C139—22no—
413C2×C4×C139—21no—
414C2×C4×C139—21no—
415C2×C4×C139—21no—
416C2×C4×C139—42no—
417C2×C4×C139—42no—
418C2×C4×C139—42no—
419C2×C4×C139—44no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—42no—
427C2×C4×C139—41no—
428C2×C4×C139—42no—
429C2×C4×C139—41no—
430C2×C4×C139—42no—
431C2×C4×C139—41no—
432C2×C4×C139—41no—
433C2×C4×C139—41no—
434C2×C4×C139—82no—
435C2×C4×C139#12011yescharacteristic
436C2×C4×C139#12011yescharacteristic
437C2×C4×C139C22×D411yescharacteristic
438C2×C4×C139C22×D411yescharacteristic
439C2×C4×C139C2×#4111yescharacteristic
440C2×C4×C139C2×#4111yescharacteristic
441C2×C4×C139H(5,𝔽2)11yescharacteristic
442C2×C4×C139H(5,𝔽2)11yescharacteristic
443C8×C139—41no—
444C8×C139—41no—
445C8×C139—41no—
446C8×C139—41no—
447C22×C139—21no—
448C22×C139—21no—
449C22×C139—21no—
450C22×C139—21no—
451C22×C139—22no—
452C22×C139—21no—
453C22×C139—21no—
454C22×C139—21no—
455C22×C139—21no—
456C22×C139—41no—
457C22×C139—41no—
458C22×C139—41no—
459C22×C139—41no—
460C22×C139—42no—
461C22×C139—41no—
462C22×C139—42no—
463C22×C139—41no—
464C22×C139—42no—
465C22×C139—41no—
466C22×C139—41no—
467C22×C139—81no—
468C22×C139—81no—
469C22×C139—82no—
470C22×C139—82no—
471C22×C139—84no—
472C22×C139—164no—
473C22×C139C2×#12011yescharacteristic
474C22×C139#54611yescharacteristic
475C22×C139#54611yescharacteristic
476C4×C139—21no—
477C4×C139—21no—
478C4×C139—22no—
479C4×C139—42no—
480C4×C139—41no—
481C4×C139—41no—
482C4×C139—41no—
483C4×C139—42no—
484C4×C139—41no—
485C4×C139—81no—
486C4×C139—81no—
487C4×C139—81no—
488C4×C139C2×#12311yescharacteristic
489C4×C139#53411yescharacteristic
490C4×C139#54611yescharacteristic
491C4×C139#54611yescharacteristic
492C2×C139—21no—
493C2×C139—21no—
494C2×C139—41no—
495C2×C139—41no—
496C2×C139—42no—
497C2×C139—81no—
498C2×C139—82no—
499C2×C139—81no—
500C2×C139#240511yescharacteristic
501C2×C139#301811yescharacteristic
502C2×C139#301911yescharacteristic
503#24031C13911yesmaximal, characteristic, direct product factor, Sylow
504C139#2403111yescharacteristic, direct product factor, Sylow
505#3488C2×C13911yescharacteristic
506#3093C2×C13911yescharacteristic, complemented
507#2896C2×C13911yescharacteristic, complemented
508#2500C2×C13911yescharacteristic, complemented
509#2040C2×C13911yescharacteristic, complemented
510#2039C2×C13911yescharacteristic, complemented
511#2037C2×C13911yescharacteristic, complemented
512#2037C2×C13911yescharacteristic, complemented
513#1900C2×C13911yescharacteristic, complemented
514#1871C2×C13911yescharacteristic, complemented
515#1860C2×C13911yescharacteristic, complemented
516#1859C2×C13911yescharacteristic, complemented
517#1792C2×C13911yescharacteristic, complemented
518#1792C2×C13911yescharacteristic, complemented
519#1789C2×C13911yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C13911yescharacteristic
521C22×#41C22×C13911yescharacteristic
522C22×M16C22×C13911yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C13911yescharacteristic
531#535—21no—
532#535C22×C13911yescharacteristic
533#525—21no—
534#525C22×C13911yescharacteristic
535C2×#121—21no—
536C2×#121C22×C13911yescharacteristic
537#520C22×C13911yescharacteristic
538C2×#117C22×C13911yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C13911yescharacteristic, complemented
544#428C22×C13911yescharacteristic, complemented
545C2×#104C22×C13911yescharacteristic
546C2×#104C22×C13911yescharacteristic
547C2×#104C22×C13911yescharacteristic, complemented
548C2×#104C22×C13911yescharacteristic, complemented
549C2×#104C22×C13911yescharacteristic, complemented
550C2×#104C22×C13911yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C13911yescharacteristic
554#417C22×C13911yescharacteristic
555#417C22×C13911yescharacteristic, complemented
556#417C22×C13911yescharacteristic, complemented
557#417C22×C13911yescharacteristic, complemented
558#417C22×C13911yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C13911yescharacteristic, complemented
562C2×#100C22×C13911yescharacteristic, complemented
563#407C22×C13911yescharacteristic, complemented
564#394—22no—
565#390C22×C13911yescharacteristic, complemented
566#390C22×C13911yescharacteristic, complemented
567#388—22no—
568#384C22×C13911yescharacteristic, complemented
569#382C22×C13911yescharacteristic, complemented
570C4×C22⋊C4C22×C13911yescharacteristic, complemented
571#343C22×C13911yescharacteristic, complemented
572#343C22×C13911yescharacteristic, complemented
573#339C22×C13911yescharacteristic, complemented
574#339C22×C13911yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C13911yescharacteristic
588C2×#41D4×C13911yescharacteristic
589C2×#41C23×C13911yescharacteristic
590C2×#41C23×C13911yescharacteristic
591C2×#41C23×C13911yescharacteristic
592C22×Q8D4×C13911yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C13911yescharacteristic
599C22×D4D4×C13912yes—
600C22×D4C23×C13911yescharacteristic
601C23×C4—21no—
602C23×C4C23×C13911yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C13911yescharacteristic
607C2×M16C23×C13911yescharacteristic
608C2×M16C23×C13911yescharacteristic
609C2×M16C23×C13911yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C13911yescharacteristic
621C22⋊Q8D4×C13911yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C13911yescharacteristic
637#121D4×C13911yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C13911yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C4⋊C4C23×C13911yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C13912yes—
667C2×C42—21no—
668C2×C42C23×C13911yescharacteristic
669C2×C42C23×C13911yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C13912yes—
701C24C2×D4×C13911yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C13912yes—
725#41#41×C13912yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C13911yescharacteristic
730C2×Q8C2×D4×C13911yescharacteristic
731C2×Q8C2×D4×C13911yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C13911yescharacteristic
766C2×D4C2×D4×C13911yescharacteristic
767C2×D4C2×D4×C13911yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C13911yescharacteristic
787C22×C4C2×D4×C13911yescharacteristic
788C22×C4C2×D4×C13911yescharacteristic
789C22×C4C2×D4×C13911yescharacteristic
790C22×C4C2×D4×C13911yescharacteristic
791C22×C4C2×D4×C13912yes—
792C22×C4C24×C13911yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C13911yescharacteristic
819C4⋊C4C2×D4×C13911yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C13911yescharacteristic
864C23#120×C13911yescharacteristic
865C23C22×D4×C13911yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C13912yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C13912yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C13911yescharacteristic
940C2×C4#120×C13911yescharacteristic
941C2×C4C22×D4×C13911yescharacteristic
942C2×C4C22×D4×C13911yescharacteristic
943C2×C4C2×#41×C13911yescharacteristic
944C2×C4C2×#41×C13911yescharacteristic
945C2×C4H(5,𝔽2)×C13911yescharacteristic
946C2×C4H(5,𝔽2)×C13911yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C13911yescharacteristic
978C22#546×C13911yescharacteristic
979C22#546×C13911yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C13911yescharacteristic
993C4#534×C13911yescharacteristic
994C4#546×C13911yescharacteristic
995C4#546×C13911yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#2405×C13911yescharacteristic
1005C2#3018×C13911yescharacteristic
1006C2#3019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3488×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3093×C139C2semidirect
3. #2896×C139C2semidirect
4. #2500×C139C2semidirect
5. #2040×C139C2semidirect
6. #2039×C139C2semidirect
7. #2037×C139C2semidirect
8. #2037×C139C2semidirect
9. #1900×C139C2semidirect
10. #1871×C139C2semidirect
11. #1860×C139C2semidirect
12. #1859×C139C2semidirect
13. #1792×C139C2semidirect
14. #1792×C139C2semidirect
15. #1789×C139C2semidirect
18. C22×M16×C139C22semidirect
34. C2×#117×C139C22semidirect
39. #428×C139C22semidirect
40. #428×C139C22semidirect
43. C2×#104×C139C22semidirect
44. C2×#104×C139C22semidirect
45. C2×#104×C139C22semidirect
46. C2×#104×C139C22semidirect
51. #417×C139C22semidirect
52. #417×C139C22semidirect
53. #417×C139C22semidirect
54. #417×C139C22semidirect
57. C2×#100×C139C22semidirect
58. C2×#100×C139C22semidirect
59. #407×C139C22semidirect
61. #390×C139C22semidirect
62. #390×C139C22semidirect
64. #384×C139C22semidirect
65. #382×C139C22semidirect
66. C4×C22⋊C4×C139C22semidirect
67. #343×C139C22semidirect
68. #343×C139C22semidirect
69. #339×C139C22semidirect
70. #339×C139C22semidirect
503. #24031C139direct (N × H)
504. C139#24031direct (N × H)
506. #3093C2×C139semidirect
507. #2896C2×C139semidirect
508. #2500C2×C139semidirect
509. #2040C2×C139semidirect
510. #2039C2×C139semidirect
511. #2037C2×C139semidirect
512. #2037C2×C139semidirect
513. #1900C2×C139semidirect
514. #1871C2×C139semidirect
515. #1860C2×C139semidirect
516. #1859C2×C139semidirect
517. #1792C2×C139semidirect
518. #1792C2×C139semidirect
519. #1789C2×C139semidirect
522. C22×M16C22×C139semidirect
538. C2×#117C22×C139semidirect
543. #428C22×C139semidirect
544. #428C22×C139semidirect
547. C2×#104C22×C139semidirect
548. C2×#104C22×C139semidirect
549. C2×#104C22×C139semidirect
550. C2×#104C22×C139semidirect
555. #417C22×C139semidirect
556. #417C22×C139semidirect
557. #417C22×C139semidirect
558. #417C22×C139semidirect
561. C2×#100C22×C139semidirect
562. C2×#100C22×C139semidirect
563. #407C22×C139semidirect
565. #390C22×C139semidirect
566. #390C22×C139semidirect
568. #384C22×C139semidirect
569. #382C22×C139semidirect
570. C4×C22⋊C4C22×C139semidirect
571. #343C22×C139semidirect
572. #343C22×C139semidirect
573. #339C22×C139semidirect
574. #339C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3488×C1392
#3093×C1392
#2896×C1392
#2500×C1392
#2040×C1392
#2039×C1392
#2037×C1392
#1900×C1392
#1871×C1392
#1860×C1392
#1859×C1392
#1792×C1392
#1789×C1392
#24031139