Finite Group Databasebeta

← C139×#18930 #48013526

Subgroups — C139×#18930 #48013526

Order 35584.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543×C139C211yesmaximal, characteristic, complemented
2#3251×C139C211yesmaximal, characteristic, complemented
3#3212×C139C211yesmaximal, characteristic, complemented
4#3205×C139C211yesmaximal, characteristic, complemented
5#1642×C139C211yesmaximal, characteristic, complemented
6#1641×C139C211yesmaximal, characteristic, complemented
7#1640×C139C211yesmaximal, characteristic, complemented
8#1639×C139C211yesmaximal, characteristic, complemented
9#1621×C139C211yesmaximal, characteristic, complemented
10#1621×C139C211yesmaximal, characteristic, complemented
11#1620×C139C211yesmaximal, characteristic, complemented
12#1619×C139C211yesmaximal, characteristic, complemented
13#1545×C139C211yesmaximal, characteristic, complemented
14#1495×C139C211yesmaximal, characteristic, complemented
15#1482×C139C211yesmaximal, characteristic, complemented
16#560×C139—22no—
17#559×C139C2211yescharacteristic
18#550×C139C2211yescharacteristic
19#550×C139C2211yescharacteristic
20#546×C139—21no—
21#546×C139—21no—
22D42×C139—21no—
23D42×C139—21no—
24D42×C139C2211yescharacteristic
25#540×C139—21no—
26#540×C139—21no—
27#535×C139—21no—
28#535×C139—21no—
29#534×C139—22no—
30#532×C139C2211yescharacteristic, complemented
31C2×#127×C139C2211yescharacteristic
32#529×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34#495×C139—21no—
35#493×C139C2211yescharacteristic
36#493×C139C2211yescharacteristic, complemented
37#488×C139—21no—
38#486×C139C2211yescharacteristic
39#486×C139C2211yescharacteristic, complemented
40#478×C139—21no—
41#475×C139C2211yescharacteristic, complemented
42#474×C139C2211yescharacteristic, complemented
43#469×C139—21no—
44#468×C139—21no—
45#463×C139—21no—
46#462×C139C2211yescharacteristic, complemented
47#461×C139C2211yescharacteristic, complemented
48#460×C139C2211yescharacteristic, complemented
49#460×C139C2211yescharacteristic, complemented
50#459×C139—22no—
51#459×C139C2211yescharacteristic, complemented
52#459×C139C2211yescharacteristic, complemented
53#452×C139—21no—
54#449×C139—21no—
55#447×C139—22no—
56#431×C139C2211yescharacteristic, complemented
57#431×C139C2211yescharacteristic, complemented
58#423×C139C2211yescharacteristic, complemented
59#331×C139C2211yescharacteristic
60#331×C139C2211yescharacteristic
61#331×C139C2211yescharacteristic, complemented
62#331×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64Q8⋊C8×C139C2211yescharacteristic, complemented
65Q8⋊C8×C139C2211yescharacteristic, complemented
66Q8⋊C8×C139C2211yescharacteristic, complemented
67D4⋊C8×C139C2211yescharacteristic, complemented
68D4⋊C8×C139C2211yescharacteristic, complemented
69D4⋊C8×C139C2211yescharacteristic, complemented
70D4⋊C8×C139C2211yescharacteristic, complemented
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—21no—
74C22×D4×C139—22no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139D412yes—
80C2×Q16×C139—21no—
81C2×SD16×C139—21no—
82C2×SD16×C139—21no—
83C2×SD16×C139—21no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—21no—
87C2×D8×C139—21no—
88C2×M16×C139—21no—
89C4⋊Q8×C139C2311yescharacteristic
90#127×C139—21no—
91#127×C139—21no—
92#127×C139—21no—
93#127×C139—21no—
94#127×C139D412yes—
95#127×C139C2311yescharacteristic
96#127×C139C2311yescharacteristic
97#127×C139C2311yescharacteristic
98#126×C139—21no—
99#126×C139—21no—
100#125×C139D411yescharacteristic
101#125×C139D411yescharacteristic
102#124×C139—21no—
103#124×C139—21no—
104#124×C139—21no—
105#124×C139D411yescharacteristic
106#124×C139D411yescharacteristic
107#123×C139—22no—
108#123×C139—22no—
109#123×C139—22no—
110#123×C139—22no—
111#123×C139—21no—
112#123×C139—21no—
113C22⋊Q8×C139D411yescharacteristic
114C22⋊Q8×C139D411yescharacteristic
115#121×C139—22no—
116#121×C139—22no—
117#121×C139—22no—
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×C139D411yescharacteristic
130#121×C139D411yescharacteristic
131#120×C139—22no—
132#120×C139—22no—
133#120×C139—22no—
134#120×C139—22no—
135#120×C139—22no—
136#120×C139—22no—
137C4×Q8×C139C2311yescharacteristic
138C4×Q8×C139C2311yescharacteristic
139C4×D4×C139—21no—
140C4×D4×C139—21no—
141C4×D4×C139—21no—
142C4×D4×C139—21no—
143C4×D4×C139—21no—
144C4×D4×C139—21no—
145C4×D4×C139—21no—
146C4×D4×C139—21no—
147C4×D4×C139C2311yescharacteristic
148C4×D4×C139C2311yescharacteristic
149#117×C139—21no—
150#117×C139—21no—
151C2×C22⋊C4×C139—22no—
152C2×C42×C139C2311yescharacteristic
153#107×C139—21no—
154#106×C139—21no—
155C4⋊C8×C139—21no—
156C4⋊C8×C139—21no—
157C4⋊C8×C139C2311yescharacteristic
158C4⋊C8×C139C2311yescharacteristic
159C4⋊C8×C139C2311yescharacteristic
160C4⋊C8×C139C2311yescharacteristic
161#103×C139—21no—
162#103×C139—21no—
163#103×C139—21no—
164#102×C139—22no—
165#102×C139—22no—
166#102×C139—21no—
167#102×C139—21no—
168#102×C139—21no—
169#102×C139—21no—
170#102×C139—21no—
171C22⋊C8×C139—21no—
172C22⋊C8×C139—21no—
173C4×C8×C139—21no—
174C4×C8×C139C2311yescharacteristic
175C4×C8×C139C2311yescharacteristic
176C24×C139—22no—
177C24×C139—22no—
178#41×C139—81no—
179#41×C139—81no—
180#41×C139—81no—
181#41×C139—81no—
182#41×C139—81no—
183#41×C139—81no—
184C2×Q8×C139—21no—
185C2×Q8×C139C2×D411yescharacteristic
186C2×Q8×C139C2×D411yescharacteristic
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—22no—
190C2×D4×C139—22no—
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—22no—
194C2×D4×C139—22no—
195C2×D4×C139—22no—
196C2×D4×C139—22no—
197C2×D4×C139—22no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—41no—
206C2×D4×C139—81no—
207C2×D4×C139—81no—
208C2×D4×C139—81no—
209C2×D4×C139—81no—
210C2×D4×C139—81no—
211C2×D4×C139—81no—
212C2×D4×C139—81no—
213C2×D4×C139—81no—
214C2×D4×C139—82no—
215C2×D4×C139—84no—
216C2×D4×C139C2×D411yescharacteristic
217C2×D4×C139C2×D411yescharacteristic
218C2×D4×C139C2×D412yes—
219C2×D4×C139C2×D412yes—
220C22×C4×C139—22no—
221C22×C4×C139—22no—
222C22×C4×C139—22no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—41no—
226C22×C4×C139C2×D411yescharacteristic
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229Q16×C139—81no—
230SD16×C139—81no—
231SD16×C139—81no—
232SD16×C139—81no—
233D8×C139—81no—
234D8×C139—81no—
235D8×C139—82no—
236D8×C139—82no—
237M16×C139—81no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139C2×D411yescharacteristic
255C4⋊C4×C139C2×D411yescharacteristic
256C4⋊C4×C139C2×D411yescharacteristic
257C4⋊C4×C139C2×D411yescharacteristic
258C22⋊C4×C139—22no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—22no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—22no—
264C22⋊C4×C139—21no—
265C22⋊C4×C139—21no—
266C22⋊C4×C139—21no—
267C22⋊C4×C139—21no—
268C22⋊C4×C139—21no—
269C22⋊C4×C139—21no—
270C22⋊C4×C139—21no—
271C22⋊C4×C139—21no—
272C22⋊C4×C139—21no—
273C22⋊C4×C139—21no—
274C22⋊C4×C139—41no—
275C22⋊C4×C139—41no—
276C42×C139—21no—
277C42×C139—21no—
278C42×C139C2×D411yescharacteristic
279C42×C139C2×D411yescharacteristic
280C42×C139C2×D411yescharacteristic
281C42×C139C2411yescharacteristic
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—22no—
285C23×C139—22no—
286C23×C139—44no—
287C23×C139—41no—
288C23×C139—82no—
289C23×C139—82no—
290C23×C139—82no—
291C23×C139—82no—
292C23×C139—82no—
293C23×C139#12011yescharacteristic
294Q8×C139—21no—
295Q8×C139—21no—
296Q8×C139—21no—
297Q8×C139—21no—
298Q8×C139—41no—
299Q8×C139—41no—
300D4×C139—21no—
301D4×C139—21no—
302D4×C139—21no—
303D4×C139—21no—
304D4×C139—42no—
305D4×C139—42no—
306D4×C139—42no—
307D4×C139—42no—
308D4×C139—42no—
309D4×C139—41no—
310D4×C139—41no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—82no—
322D4×C139—82no—
323D4×C139—82no—
324D4×C139—82no—
325D4×C139—82no—
326D4×C139—82no—
327D4×C139—82no—
328D4×C139—82no—
329D4×C139—82no—
330D4×C139—82no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—82no—
348C2×C4×C139—82no—
349C2×C4×C139—82no—
350C2×C4×C139—82no—
351C2×C4×C139#12011yescharacteristic
352C2×C4×C139#12011yescharacteristic
353C2×C4×C139#12011yescharacteristic
354C2×C4×C139C22×D411yescharacteristic
355C2×C4×C139C22×D411yescharacteristic
356C2×C4×C139C22×D411yescharacteristic
357C8×C139—41no—
358C8×C139—41no—
359C8×C139—41no—
360C8×C139—41no—
361C8×C139—41no—
362C8×C139—41no—
363C22×C139—21no—
364C22×C139—21no—
365C22×C139—21no—
366C22×C139—41no—
367C22×C139—42no—
368C22×C139—41no—
369C22×C139—42no—
370C22×C139—41no—
371C22×C139—42no—
372C22×C139—41no—
373C22×C139—42no—
374C22×C139—42no—
375C22×C139—41no—
376C22×C139—41no—
377C22×C139—42no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—164no—
382C22×C139—164no—
383C22×C139C2×#12011yescharacteristic
384C4×C139—21no—
385C4×C139—21no—
386C4×C139—21no—
387C4×C139—21no—
388C4×C139—41no—
389C4×C139—41no—
390C4×C139—41no—
391C4×C139—41no—
392C4×C139—41no—
393C4×C139—41no—
394C4×C139—81no—
395C4×C139#57611yescharacteristic
396C4×C139#57611yescharacteristic
397C4×C139#57611yescharacteristic
398C4×C139#57711yescharacteristic
399C2×C139—41no—
400C2×C139—82no—
401C2×C139—81no—
402C2×C139—81no—
403C2×C139—82no—
404C2×C139—161no—
405C2×C139#300811yescharacteristic
406C2×C139#301211yescharacteristic
407C2×C139#301911yescharacteristic
408#18930C13911yesmaximal, characteristic, direct product factor, Sylow
409C139#1893011yescharacteristic, direct product factor, Sylow
410#3543C2×C13911yescharacteristic, complemented
411#3251C2×C13911yescharacteristic, complemented
412#3212C2×C13911yescharacteristic, complemented
413#3205C2×C13911yescharacteristic, complemented
414#1642C2×C13911yescharacteristic, complemented
415#1641C2×C13911yescharacteristic, complemented
416#1640C2×C13911yescharacteristic, complemented
417#1639C2×C13911yescharacteristic, complemented
418#1621C2×C13911yescharacteristic, complemented
419#1621C2×C13911yescharacteristic, complemented
420#1620C2×C13911yescharacteristic, complemented
421#1619C2×C13911yescharacteristic, complemented
422#1545C2×C13911yescharacteristic, complemented
423#1495C2×C13911yescharacteristic, complemented
424#1482C2×C13911yescharacteristic, complemented
425#560—22no—
426#559C22×C13911yescharacteristic
427#550C22×C13911yescharacteristic
428#550C22×C13911yescharacteristic
429#546—21no—
430#546—21no—
431D42—21no—
432D42—21no—
433D42C22×C13911yescharacteristic
434#540—21no—
435#540—21no—
436#535—21no—
437#535—21no—
438#534—22no—
439#532C22×C13911yescharacteristic, complemented
440C2×#127C22×C13911yescharacteristic
441#529C22×C13911yescharacteristic
442#529C22×C13911yescharacteristic
443#495—21no—
444#493C22×C13911yescharacteristic
445#493C22×C13911yescharacteristic, complemented
446#488—21no—
447#486C22×C13911yescharacteristic
448#486C22×C13911yescharacteristic, complemented
449#478—21no—
450#475C22×C13911yescharacteristic, complemented
451#474C22×C13911yescharacteristic, complemented
452#469—21no—
453#468—21no—
454#463—21no—
455#462C22×C13911yescharacteristic, complemented
456#461C22×C13911yescharacteristic, complemented
457#460C22×C13911yescharacteristic, complemented
458#460C22×C13911yescharacteristic, complemented
459#459—22no—
460#459C22×C13911yescharacteristic, complemented
461#459C22×C13911yescharacteristic, complemented
462#452—21no—
463#449—21no—
464#447—22no—
465#431C22×C13911yescharacteristic, complemented
466#431C22×C13911yescharacteristic, complemented
467#423C22×C13911yescharacteristic, complemented
468#331C22×C13911yescharacteristic
469#331C22×C13911yescharacteristic
470#331C22×C13911yescharacteristic, complemented
471#331C22×C13911yescharacteristic, complemented
472Q8⋊C8C22×C13911yescharacteristic, complemented
473Q8⋊C8C22×C13911yescharacteristic, complemented
474Q8⋊C8C22×C13911yescharacteristic, complemented
475Q8⋊C8C22×C13911yescharacteristic, complemented
476D4⋊C8C22×C13911yescharacteristic, complemented
477D4⋊C8C22×C13911yescharacteristic, complemented
478D4⋊C8C22×C13911yescharacteristic, complemented
479D4⋊C8C22×C13911yescharacteristic, complemented
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C13912yes—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—21no—
496C2×D8—21no—
497C2×M16—21no—
498C4⋊Q8C23×C13911yescharacteristic
499#127—21no—
500#127—21no—
501#127—21no—
502#127—21no—
503#127D4×C13912yes—
504#127C23×C13911yescharacteristic
505#127C23×C13911yescharacteristic
506#127C23×C13911yescharacteristic
507#126—21no—
508#126—21no—
509#125D4×C13911yescharacteristic
510#125D4×C13911yescharacteristic
511#124—21no—
512#124—21no—
513#124—21no—
514#124D4×C13911yescharacteristic
515#124D4×C13911yescharacteristic
516#123—22no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—21no—
521#123—21no—
522C22⋊Q8D4×C13911yescharacteristic
523C22⋊Q8D4×C13911yescharacteristic
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121D4×C13911yescharacteristic
539#121D4×C13911yescharacteristic
540#120—22no—
541#120—22no—
542#120—22no—
543#120—22no—
544#120—22no—
545#120—22no—
546C4×Q8C23×C13911yescharacteristic
547C4×Q8C23×C13911yescharacteristic
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C23×C13911yescharacteristic
557C4×D4C23×C13911yescharacteristic
558#117—21no—
559#117—21no—
560C2×C22⋊C4—22no—
561C2×C42C23×C13911yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8C23×C13911yescharacteristic
567C4⋊C8C23×C13911yescharacteristic
568C4⋊C8C23×C13911yescharacteristic
569C4⋊C8C23×C13911yescharacteristic
570#103—21no—
571#103—21no—
572#103—21no—
573#102—22no—
574#102—22no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C4×C8—21no—
583C4×C8C23×C13911yescharacteristic
584C4×C8C23×C13911yescharacteristic
585C24—22no—
586C24—22no—
587#41—81no—
588#41—81no—
589#41—81no—
590#41—81no—
591#41—81no—
592#41—81no—
593C2×Q8—21no—
594C2×Q8C2×D4×C13911yescharacteristic
595C2×Q8C2×D4×C13911yescharacteristic
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—82no—
624C2×D4—84no—
625C2×D4C2×D4×C13911yescharacteristic
626C2×D4C2×D4×C13911yescharacteristic
627C2×D4C2×D4×C13912yes—
628C2×D4C2×D4×C13912yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—41no—
635C22×C4C2×D4×C13911yescharacteristic
636C22×C4C2×D4×C13911yescharacteristic
637C22×C4C2×D4×C13911yescharacteristic
638Q16—81no—
639SD16—81no—
640SD16—81no—
641SD16—81no—
642D8—81no—
643D8—81no—
644D8—82no—
645D8—82no—
646M16—81no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C13911yescharacteristic
664C4⋊C4C2×D4×C13911yescharacteristic
665C4⋊C4C2×D4×C13911yescharacteristic
666C4⋊C4C2×D4×C13911yescharacteristic
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—21no—
686C42—21no—
687C42C2×D4×C13911yescharacteristic
688C42C2×D4×C13911yescharacteristic
689C42C2×D4×C13911yescharacteristic
690C42C24×C13911yescharacteristic
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—82no—
698C23—82no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23#120×C13911yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—41no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—82no—
731D4—82no—
732D4—82no—
733D4—82no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—82no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4#120×C13911yescharacteristic
761C2×C4#120×C13911yescharacteristic
762C2×C4#120×C13911yescharacteristic
763C2×C4C22×D4×C13911yescharacteristic
764C2×C4C22×D4×C13911yescharacteristic
765C2×C4C22×D4×C13911yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—164no—
791C22—164no—
792C22C2×#120×C13911yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4#576×C13911yescharacteristic
805C4#576×C13911yescharacteristic
806C4#576×C13911yescharacteristic
807C4#577×C13911yescharacteristic
808C2—41no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2—82no—
813C2—161no—
814C2#3008×C13911yescharacteristic
815C2#3012×C13911yescharacteristic
816C2#3019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3543×C139C2semidirect
2. #3251×C139C2semidirect
3. #3212×C139C2semidirect
4. #3205×C139C2semidirect
5. #1642×C139C2semidirect
6. #1641×C139C2semidirect
7. #1640×C139C2semidirect
8. #1639×C139C2semidirect
9. #1621×C139C2semidirect
10. #1621×C139C2semidirect
11. #1620×C139C2semidirect
12. #1619×C139C2semidirect
13. #1545×C139C2semidirect
14. #1495×C139C2semidirect
15. #1482×C139C2semidirect
30. #532×C139C22semidirect
36. #493×C139C22semidirect
39. #486×C139C22semidirect
41. #475×C139C22semidirect
42. #474×C139C22semidirect
46. #462×C139C22semidirect
47. #461×C139C22semidirect
48. #460×C139C22semidirect
49. #460×C139C22semidirect
51. #459×C139C22semidirect
52. #459×C139C22semidirect
56. #431×C139C22semidirect
57. #431×C139C22semidirect
58. #423×C139C22semidirect
61. #331×C139C22semidirect
62. #331×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
64. Q8⋊C8×C139C22semidirect
65. Q8⋊C8×C139C22semidirect
66. Q8⋊C8×C139C22semidirect
67. D4⋊C8×C139C22semidirect
68. D4⋊C8×C139C22semidirect
69. D4⋊C8×C139C22semidirect
70. D4⋊C8×C139C22semidirect
408. #18930C139direct (N × H)
409. C139#18930direct (N × H)
410. #3543C2×C139semidirect
411. #3251C2×C139semidirect
412. #3212C2×C139semidirect
413. #3205C2×C139semidirect
414. #1642C2×C139semidirect
415. #1641C2×C139semidirect
416. #1640C2×C139semidirect
417. #1639C2×C139semidirect
418. #1621C2×C139semidirect
419. #1621C2×C139semidirect
420. #1620C2×C139semidirect
421. #1619C2×C139semidirect
422. #1545C2×C139semidirect
423. #1495C2×C139semidirect
424. #1482C2×C139semidirect
439. #532C22×C139semidirect
445. #493C22×C139semidirect
448. #486C22×C139semidirect
450. #475C22×C139semidirect
451. #474C22×C139semidirect
455. #462C22×C139semidirect
456. #461C22×C139semidirect
457. #460C22×C139semidirect
458. #460C22×C139semidirect
460. #459C22×C139semidirect
461. #459C22×C139semidirect
465. #431C22×C139semidirect
466. #431C22×C139semidirect
467. #423C22×C139semidirect
470. #331C22×C139semidirect
471. #331C22×C139semidirect
472. Q8⋊C8C22×C139semidirect
473. Q8⋊C8C22×C139semidirect
474. Q8⋊C8C22×C139semidirect
475. Q8⋊C8C22×C139semidirect
476. D4⋊C8C22×C139semidirect
477. D4⋊C8C22×C139semidirect
478. D4⋊C8C22×C139semidirect
479. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3543×C1392
#3251×C1392
#3212×C1392
#3205×C1392
#1642×C1392
#1641×C1392
#1640×C1392
#1639×C1392
#1621×C1392
#1620×C1392
#1619×C1392
#1545×C1392
#1495×C1392
#1482×C1392
#18930139