Finite Group Databasebeta

← C139×#18974 #48013570

Subgroups — C139×#18974 #48013570

Order 35584.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C139C211yesmaximal, characteristic
2#3254×C139C211yesmaximal, characteristic, complemented
3#3248×C139C211yesmaximal, characteristic, complemented
4#3228×C139C211yesmaximal, characteristic, complemented
5#1654×C139C211yesmaximal, characteristic, complemented
6#1652×C139C211yesmaximal, characteristic, complemented
7#1650×C139C211yesmaximal, characteristic, complemented
8#1647×C139C211yesmaximal, characteristic, complemented
9#1642×C139C211yesmaximal, characteristic, complemented
10#1641×C139C211yesmaximal, characteristic, complemented
11#1639×C139C211yesmaximal, characteristic, complemented
12#1639×C139C211yesmaximal, characteristic, complemented
13#1547×C139C211yesmaximal, characteristic, complemented
14#1495×C139C211yesmaximal, characteristic, complemented
15#1480×C139C211yesmaximal, characteristic, complemented
16#560×C139—22no—
17#556×C139C2211yescharacteristic
18#553×C139—21no—
19#550×C139—21no—
20#550×C139C2211yescharacteristic
21#547×C139C2211yescharacteristic
22#546×C139—21no—
23#546×C139—21no—
24D42×C139C2211yescharacteristic
25#542×C139—21no—
26#538×C139—22no—
27#537×C139—21no—
28#535×C139—21no—
29#535×C139—21no—
30#533×C139C2211yescharacteristic, complemented
31#532×C139C2211yescharacteristic
32#532×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34#500×C139C2211yescharacteristic, complemented
35#498×C139C2211yescharacteristic, complemented
36#486×C139C2211yescharacteristic
37#486×C139C2211yescharacteristic
38#482×C139—22no—
39#479×C139—21no—
40#478×C139—22no—
41#477×C139—21no—
42#475×C139C2211yescharacteristic, complemented
43#474×C139C2211yescharacteristic
44#474×C139C2211yescharacteristic
45#474×C139C2211yescharacteristic, complemented
46#468×C139—21no—
47#468×C139—21no—
48#467×C139—21no—
49#465×C139—21no—
50#464×C139—21no—
51#462×C139C2211yescharacteristic, complemented
52#461×C139C2211yescharacteristic
53#461×C139C2211yescharacteristic
54#461×C139C2211yescharacteristic, complemented
55#460×C139—21no—
56#431×C139C2211yescharacteristic, complemented
57#423×C139C2211yescharacteristic, complemented
58C2×C4⋊C8×C139C2211yescharacteristic, complemented
59#332×C139C2211yescharacteristic, complemented
60#332×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic
62#331×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic, complemented
64Q8⋊C8×C139C2211yescharacteristic, complemented
65D4⋊C8×C139C2211yescharacteristic
66D4⋊C8×C139C2211yescharacteristic
67D4⋊C8×C139C2211yescharacteristic
68D4⋊C8×C139C2211yescharacteristic
69D4⋊C8×C139C2211yescharacteristic, complemented
70D4⋊C8×C139C2211yescharacteristic, complemented
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—21no—
74C2×#41×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C2×Q16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139—21no—
80C2×SD16×C139—21no—
81C2×M16×C139—21no—
82C22×C8×C139—21no—
83C4⋊Q8×C139D411yescharacteristic
84C4⋊Q8×C139C2311yescharacteristic
85C4⋊Q8×C139C2311yescharacteristic
86C4⋊Q8×C139C2311yescharacteristic
87#127×C139—22no—
88#127×C139—21no—
89#127×C139D411yescharacteristic
90#127×C139C2311yescharacteristic
91#126×C139—22no—
92#126×C139—22no—
93#126×C139—21no—
94#125×C139—21no—
95#125×C139D411yescharacteristic
96#124×C139—22no—
97#124×C139—21no—
98#124×C139—21no—
99#124×C139—21no—
100#124×C139D411yescharacteristic
101#123×C139—22no—
102#123×C139—22no—
103#123×C139—21no—
104#123×C139—22no—
105C22⋊Q8×C139—22no—
106C22⋊Q8×C139—21no—
107C22⋊Q8×C139—21no—
108C22⋊Q8×C139—21no—
109C22⋊Q8×C139—21no—
110C22⋊Q8×C139D411yescharacteristic
111#121×C139—22no—
112#121×C139—22no—
113#121×C139—22no—
114#121×C139—22no—
115#121×C139—22no—
116#121×C139—21no—
117#121×C139—22no—
118#121×C139—21no—
119#121×C139—21no—
120#121×C139—21no—
121#121×C139—21no—
122#121×C139—21no—
123#121×C139D411yescharacteristic
124#121×C139D411yescharacteristic
125#121×C139D411yescharacteristic
126#121×C139D412yes—
127#120×C139—22no—
128#120×C139—22no—
129#120×C139—22no—
130#120×C139—22no—
131C4×Q8×C139—21no—
132C4×Q8×C139—21no—
133C4×Q8×C139—21no—
134C4×Q8×C139C2311yescharacteristic
135C4×D4×C139—22no—
136C4×D4×C139—21no—
137C4×D4×C139—21no—
138C4×D4×C139—21no—
139C4×D4×C139—21no—
140C4×D4×C139D412yes—
141C4×D4×C139C2311yescharacteristic
142C4×D4×C139C2311yescharacteristic
143C4×D4×C139C2311yescharacteristic
144#117×C139—21no—
145#117×C139—21no—
146#117×C139—21no—
147C2×C4⋊C4×C139—21no—
148C2×C22⋊C4×C139—22no—
149C2×C42×C139C2311yescharacteristic
150#107×C139—21no—
151#107×C139—21no—
152#107×C139—21no—
153#107×C139—22no—
154#106×C139—21no—
155#106×C139—22no—
156C4⋊C8×C139—21no—
157C4⋊C8×C139—21no—
158C4⋊C8×C139—21no—
159C4⋊C8×C139C2311yescharacteristic
160C4⋊C8×C139C2311yescharacteristic
161C4⋊C8×C139C2311yescharacteristic
162C4⋊C8×C139C2311yescharacteristic
163#103×C139—21no—
164#103×C139—21no—
165#103×C139—21no—
166#103×C139—21no—
167#103×C139—21no—
168#102×C139—21no—
169#102×C139—21no—
170#102×C139—21no—
171#102×C139—22no—
172#102×C139—22no—
173C22⋊C8×C139—21no—
174C4×C8×C139C2311yescharacteristic
175C4×C8×C139C2311yescharacteristic
176C24×C139—22no—
177#41×C139—81no—
178#41×C139—81no—
179#41×C139—81no—
180#41×C139—81no—
181#41×C139—81no—
182#41×C139—81no—
183#41×C139—81no—
184#41×C139—81no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139C2×D411yescharacteristic
190C2×D4×C139—22no—
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—22no—
194C2×D4×C139—22no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
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—81no—
204C2×D4×C139—81no—
205C2×D4×C139—81no—
206C2×D4×C139—81no—
207C2×D4×C139C2×D411yescharacteristic
208C2×D4×C139C2×D411yescharacteristic
209C2×D4×C139C2×D411yescharacteristic
210C2×D4×C139C2×D412yes—
211C22×C4×C139—22no—
212C22×C4×C139—22no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—22no—
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220Q16×C139—81no—
221SD16×C139—81no—
222SD16×C139—81no—
223SD16×C139—81no—
224M16×C139—81no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—81no—
232C4⋊C4×C139—22no—
233C4⋊C4×C139—22no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—41no—
245C4⋊C4×C139—41no—
246C4⋊C4×C139C2×D411yescharacteristic
247C4⋊C4×C139C2×D411yescharacteristic
248C4⋊C4×C139C2×D411yescharacteristic
249C4⋊C4×C139C2×D411yescharacteristic
250C4⋊C4×C139C2×D412yes—
251C22⋊C4×C139—22no—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—21no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—21no—
259C22⋊C4×C139—21no—
260C22⋊C4×C139—21no—
261C22⋊C4×C139—21no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—22no—
264C22⋊C4×C139—21no—
265C22⋊C4×C139—21no—
266C22⋊C4×C139—21no—
267C22⋊C4×C139—41no—
268C42×C139—22no—
269C42×C139—21no—
270C42×C139—41no—
271C42×C139C2×D411yescharacteristic
272C42×C139C2×D411yescharacteristic
273C42×C139C2×D411yescharacteristic
274C42×C139C2411yescharacteristic
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—22no—
278C23×C139—21no—
279C23×C139—82no—
280C23×C139—82no—
281C23×C139—82no—
282C23×C139#12011yescharacteristic
283Q8×C139—21no—
284Q8×C139—21no—
285Q8×C139—41no—
286Q8×C139—41no—
287Q8×C139—41no—
288Q8×C139—41no—
289Q8×C139—41no—
290Q8×C139—41no—
291Q8×C139—81no—
292D4×C139—21no—
293D4×C139—21no—
294D4×C139—21no—
295D4×C139—21no—
296D4×C139—21no—
297D4×C139—21no—
298D4×C139—42no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—81no—
304D4×C139—81no—
305D4×C139—81no—
306D4×C139—81no—
307D4×C139—81no—
308D4×C139—82no—
309D4×C139—82no—
310D4×C139—82no—
311D4×C139—82no—
312D4×C139—82no—
313D4×C139—82no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—22no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—82no—
334C2×C4×C139—82no—
335C2×C4×C139—82no—
336C2×C4×C139#12011yescharacteristic
337C2×C4×C139#12011yescharacteristic
338C2×C4×C139#12011yescharacteristic
339C2×C4×C139C22×D411yescharacteristic
340C2×C4×C139C22×D411yescharacteristic
341C2×C4×C139C22×D411yescharacteristic
342C8×C139—41no—
343C8×C139—41no—
344C8×C139—41no—
345C8×C139—41no—
346C8×C139—41no—
347C8×C139—41no—
348C22×C139—21no—
349C22×C139—21no—
350C22×C139—21no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—42no—
356C22×C139—42no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—42no—
360C22×C139—41no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—164no—
364C22×C139C2×#12011yescharacteristic
365C4×C139—21no—
366C4×C139—21no—
367C4×C139—21no—
368C4×C139—21no—
369C4×C139—41no—
370C4×C139—41no—
371C4×C139—41no—
372C4×C139—41no—
373C4×C139—42no—
374C4×C139—41no—
375C4×C139—81no—
376C4×C139—81no—
377C4×C139#57611yescharacteristic
378C4×C139#57611yescharacteristic
379C4×C139#57711yescharacteristic
380C4×C139#57711yescharacteristic
381C2×C139—41no—
382C2×C139—81no—
383C2×C139—82no—
384C2×C139—81no—
385C2×C139—81no—
386C2×C139#301211yescharacteristic
387C2×C139#301211yescharacteristic
388C2×C139#302211yescharacteristic
389#18974C13911yesmaximal, characteristic, direct product factor, Sylow
390C139#1897411yescharacteristic, direct product factor, Sylow
391#3546C2×C13911yescharacteristic
392#3254C2×C13911yescharacteristic, complemented
393#3248C2×C13911yescharacteristic, complemented
394#3228C2×C13911yescharacteristic, complemented
395#1654C2×C13911yescharacteristic, complemented
396#1652C2×C13911yescharacteristic, complemented
397#1650C2×C13911yescharacteristic, complemented
398#1647C2×C13911yescharacteristic, complemented
399#1642C2×C13911yescharacteristic, complemented
400#1641C2×C13911yescharacteristic, complemented
401#1639C2×C13911yescharacteristic, complemented
402#1639C2×C13911yescharacteristic, complemented
403#1547C2×C13911yescharacteristic, complemented
404#1495C2×C13911yescharacteristic, complemented
405#1480C2×C13911yescharacteristic, complemented
406#560—22no—
407#556C22×C13911yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C13911yescharacteristic
411#547C22×C13911yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C13911yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C13911yescharacteristic, complemented
421#532C22×C13911yescharacteristic
422#532C22×C13911yescharacteristic
423#529C22×C13911yescharacteristic
424#500C22×C13911yescharacteristic, complemented
425#498C22×C13911yescharacteristic, complemented
426#486C22×C13911yescharacteristic
427#486C22×C13911yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C13911yescharacteristic, complemented
433#474C22×C13911yescharacteristic
434#474C22×C13911yescharacteristic
435#474C22×C13911yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C13911yescharacteristic, complemented
442#461C22×C13911yescharacteristic
443#461C22×C13911yescharacteristic
444#461C22×C13911yescharacteristic, complemented
445#460—21no—
446#431C22×C13911yescharacteristic, complemented
447#423C22×C13911yescharacteristic, complemented
448C2×C4⋊C8C22×C13911yescharacteristic, complemented
449#332C22×C13911yescharacteristic, complemented
450#332C22×C13911yescharacteristic, complemented
451#331C22×C13911yescharacteristic
452#331C22×C13911yescharacteristic
453Q8⋊C8C22×C13911yescharacteristic, complemented
454Q8⋊C8C22×C13911yescharacteristic, complemented
455D4⋊C8C22×C13911yescharacteristic
456D4⋊C8C22×C13911yescharacteristic
457D4⋊C8C22×C13911yescharacteristic
458D4⋊C8C22×C13911yescharacteristic
459D4⋊C8C22×C13911yescharacteristic, complemented
460D4⋊C8C22×C13911yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C13911yescharacteristic
474C4⋊Q8C23×C13911yescharacteristic
475C4⋊Q8C23×C13911yescharacteristic
476C4⋊Q8C23×C13911yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C13911yescharacteristic
480#127C23×C13911yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C13911yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C13911yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C13911yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C13911yescharacteristic
514#121D4×C13911yescharacteristic
515#121D4×C13911yescharacteristic
516#121D4×C13912yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C13911yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C13912yes—
531C4×D4C23×C13911yescharacteristic
532C4×D4C23×C13911yescharacteristic
533C4×D4C23×C13911yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C13911yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C13911yescharacteristic
550C4⋊C8C23×C13911yescharacteristic
551C4⋊C8C23×C13911yescharacteristic
552C4⋊C8C23×C13911yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C13911yescharacteristic
565C4×C8C23×C13911yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C13911yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C13911yescharacteristic
598C2×D4C2×D4×C13911yescharacteristic
599C2×D4C2×D4×C13911yescharacteristic
600C2×D4C2×D4×C13912yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C13911yescharacteristic
608C22×C4C2×D4×C13911yescharacteristic
609C22×C4C2×D4×C13911yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C13911yescharacteristic
637C4⋊C4C2×D4×C13911yescharacteristic
638C4⋊C4C2×D4×C13911yescharacteristic
639C4⋊C4C2×D4×C13911yescharacteristic
640C4⋊C4C2×D4×C13912yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C13911yescharacteristic
662C42C2×D4×C13911yescharacteristic
663C42C2×D4×C13911yescharacteristic
664C42C24×C13911yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C13911yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C13911yescharacteristic
727C2×C4#120×C13911yescharacteristic
728C2×C4#120×C13911yescharacteristic
729C2×C4C22×D4×C13911yescharacteristic
730C2×C4C22×D4×C13911yescharacteristic
731C2×C4C22×D4×C13911yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C13911yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4#576×C13911yescharacteristic
768C4#576×C13911yescharacteristic
769C4#577×C13911yescharacteristic
770C4#577×C13911yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2#3012×C13911yescharacteristic
777C2#3012×C13911yescharacteristic
778C2#3022×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
prime radical#3546×C139C2
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
2. #3254×C139C2semidirect
3. #3248×C139C2semidirect
4. #3228×C139C2semidirect
5. #1654×C139C2semidirect
6. #1652×C139C2semidirect
7. #1650×C139C2semidirect
8. #1647×C139C2semidirect
9. #1642×C139C2semidirect
10. #1641×C139C2semidirect
11. #1639×C139C2semidirect
12. #1639×C139C2semidirect
13. #1547×C139C2semidirect
14. #1495×C139C2semidirect
15. #1480×C139C2semidirect
30. #533×C139C22semidirect
34. #500×C139C22semidirect
35. #498×C139C22semidirect
42. #475×C139C22semidirect
45. #474×C139C22semidirect
51. #462×C139C22semidirect
54. #461×C139C22semidirect
56. #431×C139C22semidirect
57. #423×C139C22semidirect
58. C2×C4⋊C8×C139C22semidirect
59. #332×C139C22semidirect
60. #332×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
64. Q8⋊C8×C139C22semidirect
69. D4⋊C8×C139C22semidirect
70. D4⋊C8×C139C22semidirect
389. #18974C139direct (N × H)
390. C139#18974direct (N × H)
392. #3254C2×C139semidirect
393. #3248C2×C139semidirect
394. #3228C2×C139semidirect
395. #1654C2×C139semidirect
396. #1652C2×C139semidirect
397. #1650C2×C139semidirect
398. #1647C2×C139semidirect
399. #1642C2×C139semidirect
400. #1641C2×C139semidirect
401. #1639C2×C139semidirect
402. #1639C2×C139semidirect
403. #1547C2×C139semidirect
404. #1495C2×C139semidirect
405. #1480C2×C139semidirect
420. #533C22×C139semidirect
424. #500C22×C139semidirect
425. #498C22×C139semidirect
432. #475C22×C139semidirect
435. #474C22×C139semidirect
441. #462C22×C139semidirect
444. #461C22×C139semidirect
446. #431C22×C139semidirect
447. #423C22×C139semidirect
448. C2×C4⋊C8C22×C139semidirect
449. #332C22×C139semidirect
450. #332C22×C139semidirect
453. Q8⋊C8C22×C139semidirect
454. Q8⋊C8C22×C139semidirect
459. D4⋊C8C22×C139semidirect
460. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3546×C1392
#3254×C1392
#3248×C1392
#3228×C1392
#1654×C1392
#1652×C1392
#1650×C1392
#1647×C1392
#1642×C1392
#1641×C1392
#1639×C1392
#1547×C1392
#1495×C1392
#1480×C1392
#18974139