Finite Group Databasebeta

← C139×#18444 #48013040

Subgroups — C139×#18444 #48013040

Order 35584.

908 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560×C139C211yesmaximal, characteristic
2#3234×C139C211yesmaximal, characteristic, complemented
3#3232×C139C211yesmaximal, characteristic, complemented
4#2664×C139C211yesmaximal, characteristic, complemented
5#1618×C139C211yesmaximal, characteristic, complemented
6#1616×C139C211yesmaximal, characteristic, complemented
7#1615×C139C211yesmaximal, characteristic, complemented
8#1613×C139C211yesmaximal, characteristic, complemented
9#1612×C139C211yesmaximal, characteristic, complemented
10#1610×C139C211yesmaximal, characteristic, complemented
11#1609×C139C211yesmaximal, characteristic, complemented
12#1607×C139C211yesmaximal, characteristic, complemented
13#1509×C139C211yesmaximal, characteristic, complemented
14#1502×C139C211yesmaximal, characteristic, complemented
15#1473×C139C211yesmaximal, characteristic, complemented
16#563×C139—21no—
17#560×C139—21no—
18#553×C139—21no—
19#553×C139—21no—
20#551×C139—21no—
21#547×C139—21no—
22#546×C139—21no—
23#546×C139—21no—
24#542×C139—21no—
25#539×C139—21no—
26#539×C139C2211yescharacteristic
27#538×C139—21no—
28#538×C139—21no—
29#538×C139C2211yescharacteristic
30#537×C139C2211yescharacteristic
31#534×C139C2211yescharacteristic
32#532×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34C2×#126×C139C2211yescharacteristic
35C2×#125×C139C2211yescharacteristic, complemented
36#501×C139—21no—
37#499×C139—21no—
38#490×C139—21no—
39#488×C139—21no—
40#484×C139C2211yescharacteristic, complemented
41#483×C139C2211yescharacteristic, complemented
42#481×C139C2211yescharacteristic
43#481×C139C2211yescharacteristic
44#481×C139C2211yescharacteristic, complemented
45#480×C139C2211yescharacteristic
46#480×C139C2211yescharacteristic
47#480×C139C2211yescharacteristic, complemented
48#479×C139—21no—
49#478×C139—21no—
50#478×C139—21no—
51#478×C139—21no—
52#432×C139C2211yescharacteristic, complemented
53#431×C139C2211yescharacteristic, complemented
54#400×C139C2211yescharacteristic, complemented
55#399×C139C2211yescharacteristic
56#398×C139—21no—
57#398×C139C2211yescharacteristic, complemented
58#397×C139C2211yescharacteristic
59#396×C139—21no—
60#389×C139—21no—
61#388×C139—21no—
62C4×C4⋊C4×C139C2211yescharacteristic, complemented
63#328×C139C2211yescharacteristic, complemented
64#328×C139C2211yescharacteristic, complemented
65#327×C139C2211yescharacteristic
66#327×C139C2211yescharacteristic
67#327×C139C2211yescharacteristic
68#327×C139C2211yescharacteristic
69#327×C139C2211yescharacteristic, complemented
70#327×C139C2211yescharacteristic, complemented
71#324×C139C2211yescharacteristic, complemented
72#324×C139C2211yescharacteristic, complemented
73#323×C139C2211yescharacteristic
74#323×C139C2211yescharacteristic
75C2×#41×C139—21no—
76C2×#41×C139—21no—
77C22×D4×C139—21no—
78C4⋊Q8×C139—21no—
79C4⋊Q8×C139D411yescharacteristic
80#127×C139D411yescharacteristic
81#126×C139—21no—
82#126×C139—21no—
83#126×C139—21no—
84#126×C139—21no—
85#126×C139—21no—
86#126×C139—21no—
87#126×C139—21no—
88#126×C139—21no—
89#126×C139—21no—
90#125×C139—21no—
91#125×C139—21no—
92#125×C139—21no—
93#125×C139—21no—
94#125×C139—21no—
95#125×C139—21no—
96#125×C139D411yescharacteristic
97#124×C139—21no—
98#124×C139—21no—
99#124×C139—21no—
100#124×C139—21no—
101#124×C139D411yescharacteristic
102#123×C139—21no—
103#123×C139—21no—
104#123×C139—21no—
105#123×C139—21no—
106#123×C139—21no—
107#123×C139—21no—
108#123×C139—21no—
109#123×C139—21no—
110#123×C139—21no—
111#123×C139—21no—
112#123×C139—21no—
113#123×C139—21no—
114C22⋊Q8×C139—21no—
115C22⋊Q8×C139—21no—
116C22⋊Q8×C139—21no—
117C22⋊Q8×C139—21no—
118C22⋊Q8×C139—21no—
119C22⋊Q8×C139—21no—
120C22⋊Q8×C139—21no—
121C22⋊Q8×C139C2311yescharacteristic
122#121×C139—21no—
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—21no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139—21no—
133#121×C139—21no—
134#121×C139C2311yescharacteristic
135#121×C139C2311yescharacteristic
136#121×C139C2311yescharacteristic
137#120×C139—21no—
138#120×C139—21no—
139#120×C139—21no—
140#120×C139—21no—
141#120×C139—21no—
142C4×Q8×C139D411yescharacteristic
143C4×D4×C139—21no—
144C4×D4×C139—21no—
145C4×D4×C139—21no—
146C4×D4×C139—21no—
147C4×D4×C139—21no—
148C4×D4×C139—21no—
149C4×D4×C139—21no—
150C4×D4×C139—21no—
151C4×D4×C139D411yescharacteristic
152C4×D4×C139D411yescharacteristic
153C4×D4×C139D411yescharacteristic
154#117×C139—21no—
155#117×C139—21no—
156C2×C4⋊C4×C139—21no—
157C2×C4⋊C4×C139—21no—
158C2×C4⋊C4×C139—21no—
159C2×C4⋊C4×C139—21no—
160C2×C4⋊C4×C139—21no—
161C2×C4⋊C4×C139—21no—
162C2×C4⋊C4×C139D411yescharacteristic
163C2×C4⋊C4×C139D411yescharacteristic
164C2×C4⋊C4×C139C2311yescharacteristic
165C2×C4⋊C4×C139C2311yescharacteristic
166C2×C4⋊C4×C139C2311yescharacteristic
167C2×C22⋊C4×C139—21no—
168C2×C22⋊C4×C139—21no—
169C2×C22⋊C4×C139—21no—
170C2×C22⋊C4×C139—21no—
171C2×C22⋊C4×C139D411yescharacteristic
172C2×C22⋊C4×C139D411yescharacteristic
173C2×C22⋊C4×C139C2311yescharacteristic
174C2×C42×C139—21no—
175C2×C42×C139C2311yescharacteristic
176#107×C139—21no—
177#107×C139—21no—
178#107×C139—21no—
179#107×C139—21no—
180#106×C139—21no—
181#106×C139—21no—
182#106×C139—21no—
183#106×C139—21no—
184C4⋊C8×C139—21no—
185C4⋊C8×C139—21no—
186#103×C139—21no—
187#103×C139—21no—
188#102×C139—21no—
189#102×C139—21no—
190#102×C139—21no—
191#102×C139—21no—
192#102×C139—21no—
193#102×C139—21no—
194C22⋊C8×C139C2311yescharacteristic
195C22⋊C8×C139C2311yescharacteristic
196C22⋊C8×C139C2311yescharacteristic
197C22⋊C8×C139C2311yescharacteristic
198#97×C139—21no—
199C4×C8×C139—21no—
200#95×C139—21no—
201#95×C139—21no—
202#95×C139—21no—
203#95×C139—21no—
204#95×C139C2311yescharacteristic
205#95×C139C2311yescharacteristic
206C24×C139—21no—
207C24×C139C2×D411yescharacteristic
208#41×C139—81no—
209#41×C139—81no—
210#41×C139—81no—
211#41×C139—81no—
212C2×Q8×C139—21no—
213C2×Q8×C139—21no—
214C2×Q8×C139C2×D411yescharacteristic
215C2×D4×C139—21no—
216C2×D4×C139—21no—
217C2×D4×C139—21no—
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—81no—
228C2×D4×C139—81no—
229C2×D4×C139C2×D411yescharacteristic
230C2×D4×C139C2×D411yescharacteristic
231C2×D4×C139C2×D411yescharacteristic
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—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139C2×D411yescharacteristic
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D411yescharacteristic
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2411yescharacteristic
250C2×C8×C139—21no—
251C2×C8×C139—21no—
252C2×C8×C139—21no—
253C2×C8×C139—21no—
254C4⋊C4×C139—21no—
255C4⋊C4×C139—21no—
256C4⋊C4×C139—21no—
257C4⋊C4×C139—21no—
258C4⋊C4×C139—21no—
259C4⋊C4×C139—21no—
260C4⋊C4×C139—21no—
261C4⋊C4×C139—21no—
262C4⋊C4×C139—21no—
263C4⋊C4×C139—21no—
264C4⋊C4×C139—21no—
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—42no—
276C4⋊C4×C139—42no—
277C4⋊C4×C139—41no—
278C4⋊C4×C139—41no—
279C4⋊C4×C139—41no—
280C4⋊C4×C139—41no—
281C4⋊C4×C139—81no—
282C4⋊C4×C139C2×D411yescharacteristic
283C4⋊C4×C139C2×D411yescharacteristic
284C4⋊C4×C139C2×D411yescharacteristic
285C4⋊C4×C139C2×D411yescharacteristic
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—21no—
292C22⋊C4×C139—21no—
293C22⋊C4×C139—21no—
294C22⋊C4×C139—21no—
295C22⋊C4×C139—21no—
296C22⋊C4×C139—21no—
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—21no—
304C22⋊C4×C139—21no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—21no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—42no—
312C22⋊C4×C139—81no—
313C42×C139—21no—
314C42×C139—21no—
315C42×C139—21no—
316C42×C139—81no—
317C42×C139C2×D411yescharacteristic
318C42×C139C2×D411yescharacteristic
319C42×C139C2×D411yescharacteristic
320C42×C139C2×D411yescharacteristic
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—21no—
324C23×C139—21no—
325C23×C139—21no—
326C23×C139—21no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—81no—
330C23×C139—81no—
331C23×C139—81no—
332C23×C139C22×D411yescharacteristic
333Q8×C139—41no—
334Q8×C139—81no—
335Q8×C139—81no—
336D4×C139—41no—
337D4×C139—41no—
338D4×C139—41no—
339D4×C139—41no—
340D4×C139—41no—
341D4×C139—41no—
342D4×C139—41no—
343D4×C139—41no—
344D4×C139—41no—
345D4×C139—81no—
346D4×C139—81no—
347D4×C139—81no—
348D4×C139—81no—
349D4×C139—81no—
350D4×C139—81no—
351D4×C139—81no—
352D4×C139—81no—
353D4×C139—81no—
354C2×C4×C139—21no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—21no—
363C2×C4×C139—21no—
364C2×C4×C139—21no—
365C2×C4×C139—21no—
366C2×C4×C139—21no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—41no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
382C2×C4×C139—81no—
383C2×C4×C139—81no—
384C2×C4×C139—81no—
385C2×C4×C139—81no—
386C2×C4×C139—81no—
387C2×C4×C139—81no—
388C2×C4×C139—81no—
389C2×C4×C139—81no—
390C2×C4×C139#12011yescharacteristic
391C2×C4×C139#12011yescharacteristic
392C2×C4×C139#12011yescharacteristic
393C2×C4×C139#12011yescharacteristic
394C2×C4×C139C22×D411yescharacteristic
395C2×C4×C139C22×D411yescharacteristic
396C8×C139—41no—
397C8×C139—41no—
398C8×C139—41no—
399C8×C139—41no—
400C22×C139—21no—
401C22×C139—21no—
402C22×C139—41no—
403C22×C139—41no—
404C22×C139—41no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—41no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—41no—
414C22×C139—81no—
415C22×C139—81no—
416C22×C139—162no—
417C22×C139C2×#12011yescharacteristic
418C22×C139#57611yescharacteristic
419C22×C139#57711yescharacteristic
420C4×C139—21no—
421C4×C139—21no—
422C4×C139—21no—
423C4×C139—21no—
424C4×C139—21no—
425C4×C139—21no—
426C4×C139—42no—
427C4×C139—41no—
428C4×C139—41no—
429C4×C139—41no—
430C4×C139—41no—
431C4×C139—41no—
432C4×C139—41no—
433C4×C139—41no—
434C4×C139—41no—
435C4×C139—81no—
436C4×C139—81no—
437C4×C139—81no—
438C2×C139—21no—
439C2×C139—21no—
440C2×C139—81no—
441C2×C139—81no—
442C2×C139—81no—
443C2×C139—81no—
444C2×C139#301211yescharacteristic
445C2×C139#301811yescharacteristic
446C2×C139#302811yescharacteristic
447#18444C13911yesmaximal, characteristic, direct product factor, Sylow
448C139#1844411yescharacteristic, direct product factor, Sylow
449#3560C2×C13911yescharacteristic
450#3234C2×C13911yescharacteristic, complemented
451#3232C2×C13911yescharacteristic, complemented
452#2664C2×C13911yescharacteristic, complemented
453#1618C2×C13911yescharacteristic, complemented
454#1616C2×C13911yescharacteristic, complemented
455#1615C2×C13911yescharacteristic, complemented
456#1613C2×C13911yescharacteristic, complemented
457#1612C2×C13911yescharacteristic, complemented
458#1610C2×C13911yescharacteristic, complemented
459#1609C2×C13911yescharacteristic, complemented
460#1607C2×C13911yescharacteristic, complemented
461#1509C2×C13911yescharacteristic, complemented
462#1502C2×C13911yescharacteristic, complemented
463#1473C2×C13911yescharacteristic, complemented
464#563—21no—
465#560—21no—
466#553—21no—
467#553—21no—
468#551—21no—
469#547—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#539—21no—
474#539C22×C13911yescharacteristic
475#538—21no—
476#538—21no—
477#538C22×C13911yescharacteristic
478#537C22×C13911yescharacteristic
479#534C22×C13911yescharacteristic
480#532C22×C13911yescharacteristic
481#529C22×C13911yescharacteristic
482C2×#126C22×C13911yescharacteristic
483C2×#125C22×C13911yescharacteristic, complemented
484#501—21no—
485#499—21no—
486#490—21no—
487#488—21no—
488#484C22×C13911yescharacteristic, complemented
489#483C22×C13911yescharacteristic, complemented
490#481C22×C13911yescharacteristic
491#481C22×C13911yescharacteristic
492#481C22×C13911yescharacteristic, complemented
493#480C22×C13911yescharacteristic
494#480C22×C13911yescharacteristic
495#480C22×C13911yescharacteristic, complemented
496#479—21no—
497#478—21no—
498#478—21no—
499#478—21no—
500#432C22×C13911yescharacteristic, complemented
501#431C22×C13911yescharacteristic, complemented
502#400C22×C13911yescharacteristic, complemented
503#399C22×C13911yescharacteristic
504#398—21no—
505#398C22×C13911yescharacteristic, complemented
506#397C22×C13911yescharacteristic
507#396—21no—
508#389—21no—
509#388—21no—
510C4×C4⋊C4C22×C13911yescharacteristic, complemented
511#328C22×C13911yescharacteristic, complemented
512#328C22×C13911yescharacteristic, complemented
513#327C22×C13911yescharacteristic
514#327C22×C13911yescharacteristic
515#327C22×C13911yescharacteristic
516#327C22×C13911yescharacteristic
517#327C22×C13911yescharacteristic, complemented
518#327C22×C13911yescharacteristic, complemented
519#324C22×C13911yescharacteristic, complemented
520#324C22×C13911yescharacteristic, complemented
521#323C22×C13911yescharacteristic
522#323C22×C13911yescharacteristic
523C2×#41—21no—
524C2×#41—21no—
525C22×D4—21no—
526C4⋊Q8—21no—
527C4⋊Q8D4×C13911yescharacteristic
528#127D4×C13911yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#125—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125D4×C13911yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124D4×C13911yescharacteristic
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8C23×C13911yescharacteristic
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121C23×C13911yescharacteristic
583#121C23×C13911yescharacteristic
584#121C23×C13911yescharacteristic
585#120—21no—
586#120—21no—
587#120—21no—
588#120—21no—
589#120—21no—
590C4×Q8D4×C13911yescharacteristic
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4D4×C13911yescharacteristic
600C4×D4D4×C13911yescharacteristic
601C4×D4D4×C13911yescharacteristic
602#117—21no—
603#117—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C13911yescharacteristic
611C2×C4⋊C4D4×C13911yescharacteristic
612C2×C4⋊C4C23×C13911yescharacteristic
613C2×C4⋊C4C23×C13911yescharacteristic
614C2×C4⋊C4C23×C13911yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4D4×C13911yescharacteristic
620C2×C22⋊C4D4×C13911yescharacteristic
621C2×C22⋊C4C23×C13911yescharacteristic
622C2×C42—21no—
623C2×C42C23×C13911yescharacteristic
624#107—21no—
625#107—21no—
626#107—21no—
627#107—21no—
628#106—21no—
629#106—21no—
630#106—21no—
631#106—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8C23×C13911yescharacteristic
643C22⋊C8C23×C13911yescharacteristic
644C22⋊C8C23×C13911yescharacteristic
645C22⋊C8C23×C13911yescharacteristic
646#97—21no—
647C4×C8—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95—21no—
652#95C23×C13911yescharacteristic
653#95C23×C13911yescharacteristic
654C24—21no—
655C24C2×D4×C13911yescharacteristic
656#41—81no—
657#41—81no—
658#41—81no—
659#41—81no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C13911yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C13911yescharacteristic
678C2×D4C2×D4×C13911yescharacteristic
679C2×D4C2×D4×C13911yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C2×D4×C13911yescharacteristic
693C22×C4C2×D4×C13911yescharacteristic
694C22×C4C2×D4×C13911yescharacteristic
695C22×C4C2×D4×C13911yescharacteristic
696C22×C4C2×D4×C13911yescharacteristic
697C22×C4C24×C13911yescharacteristic
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C13911yescharacteristic
731C4⋊C4C2×D4×C13911yescharacteristic
732C4⋊C4C2×D4×C13911yescharacteristic
733C4⋊C4C2×D4×C13911yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—42no—
760C22⋊C4—81no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—81no—
765C42C2×D4×C13911yescharacteristic
766C42C2×D4×C13911yescharacteristic
767C42C2×D4×C13911yescharacteristic
768C42C2×D4×C13911yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—81no—
778C23—81no—
779C23—81no—
780C23C22×D4×C13911yescharacteristic
781Q8—41no—
782Q8—81no—
783Q8—81no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—81no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
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—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4#120×C13911yescharacteristic
839C2×C4#120×C13911yescharacteristic
840C2×C4#120×C13911yescharacteristic
841C2×C4#120×C13911yescharacteristic
842C2×C4C22×D4×C13911yescharacteristic
843C2×C4C22×D4×C13911yescharacteristic
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22C2×#120×C13911yescharacteristic
866C22#576×C13911yescharacteristic
867C22#577×C13911yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—81no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#3012×C13911yescharacteristic
893C2#3018×C13911yescharacteristic
894C2#3028×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3560×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3234×C139C2semidirect
3. #3232×C139C2semidirect
4. #2664×C139C2semidirect
5. #1618×C139C2semidirect
6. #1616×C139C2semidirect
7. #1615×C139C2semidirect
8. #1613×C139C2semidirect
9. #1612×C139C2semidirect
10. #1610×C139C2semidirect
11. #1609×C139C2semidirect
12. #1607×C139C2semidirect
13. #1509×C139C2semidirect
14. #1502×C139C2semidirect
15. #1473×C139C2semidirect
35. C2×#125×C139C22semidirect
40. #484×C139C22semidirect
41. #483×C139C22semidirect
44. #481×C139C22semidirect
47. #480×C139C22semidirect
52. #432×C139C22semidirect
53. #431×C139C22semidirect
54. #400×C139C22semidirect
57. #398×C139C22semidirect
62. C4×C4⋊C4×C139C22semidirect
63. #328×C139C22semidirect
64. #328×C139C22semidirect
69. #327×C139C22semidirect
70. #327×C139C22semidirect
71. #324×C139C22semidirect
72. #324×C139C22semidirect
447. #18444C139direct (N × H)
448. C139#18444direct (N × H)
450. #3234C2×C139semidirect
451. #3232C2×C139semidirect
452. #2664C2×C139semidirect
453. #1618C2×C139semidirect
454. #1616C2×C139semidirect
455. #1615C2×C139semidirect
456. #1613C2×C139semidirect
457. #1612C2×C139semidirect
458. #1610C2×C139semidirect
459. #1609C2×C139semidirect
460. #1607C2×C139semidirect
461. #1509C2×C139semidirect
462. #1502C2×C139semidirect
463. #1473C2×C139semidirect
483. C2×#125C22×C139semidirect
488. #484C22×C139semidirect
489. #483C22×C139semidirect
492. #481C22×C139semidirect
495. #480C22×C139semidirect
500. #432C22×C139semidirect
501. #431C22×C139semidirect
502. #400C22×C139semidirect
505. #398C22×C139semidirect
510. C4×C4⋊C4C22×C139semidirect
511. #328C22×C139semidirect
512. #328C22×C139semidirect
517. #327C22×C139semidirect
518. #327C22×C139semidirect
519. #324C22×C139semidirect
520. #324C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3560×C1392
#3234×C1392
#3232×C1392
#2664×C1392
#1618×C1392
#1616×C1392
#1615×C1392
#1613×C1392
#1612×C1392
#1610×C1392
#1609×C1392
#1607×C1392
#1509×C1392
#1502×C1392
#1473×C1392
#18444139