Finite Group Databasebeta

← C139×#33552 #48028148

Subgroups — C139×#33552 #48028148

Order 35584.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3533×C139C211yesmaximal, characteristic, complemented
2#3026×C139C211yesmaximal, characteristic, complemented
3C2×#458×C139C211yesmaximal, characteristic, complemented
4#3019×C139C211yesmaximal, characteristic, complemented
5#2201×C139C212yesmaximal, complemented
6#2200×C139C212yesmaximal, complemented
7#2198×C139C212yesmaximal, complemented
8#2197×C139C212yesmaximal, complemented
9#2127×C139C211yesmaximal, characteristic, complemented
10#2121×C139C211yesmaximal, characteristic, complemented
11C2×#352×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic
13#575×C139—21no—
14#563×C139C2211yescharacteristic, complemented
15#562×C139—21no—
16#560×C139C2211yescharacteristic, complemented
17#559×C139C2211yescharacteristic, complemented
18#553×C139—21no—
19#552×C139—21no—
20#551×C139—21no—
21#551×C139C2211yescharacteristic, complemented
22#547×C139—21no—
23#546×C139—21no—
24#542×C139—21no—
25#540×C139—21no—
26#539×C139—21no—
27#538×C139—21no—
28#538×C139—21no—
29#535×C139C2211yescharacteristic
30#534×C139—21no—
31#534×C139C2211yescharacteristic
32#525×C139—21no—
33C2×#123×C139—21no—
34C2×#123×C139C2211yescharacteristic
35#458×C139—21no—
36#458×C139—21no—
37#458×C139—21no—
38#458×C139C2212yes—
39#458×C139C2212yes—
40#458×C139C2212yes—
41B(4,𝔽2)×C139—21no—
42B(4,𝔽2)×C139C2212yes—
43#455×C139—21no—
44#455×C139C2212yes—
45#453×C139—21no—
46#453×C139C2212yes—
47#421×C139—21no—
48C2×#100×C139C2211yescharacteristic
49C2×#99×C139—21no—
50C2×#99×C139—21no—
51C2×#99×C139C2211yescharacteristic
52C2×#99×C139C2211yescharacteristic
53#354×C139C2212yescomplemented
54#353×C139C2212yescomplemented
55#352×C139C2212yescomplemented
56#352×C139C2212yescomplemented
57#352×C139C2212yescomplemented
58AΣL(1,𝔽16)×C139C2212yescomplemented
59H(5,𝔽2)×C139—21no—
60H(5,𝔽2)×C139—21no—
61H(5,𝔽2)×C139—21no—
62H(5,𝔽2)×C139—42no—
63H(5,𝔽2)×C139C2312yes—
64C2×#41×C139—21no—
65C2×#41×C139—21no—
66C2×#41×C139—41no—
67C2×#41×C139D411yescharacteristic, complemented
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—41no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C23×C4×C139D411yescharacteristic, complemented
74#137×C139—22no—
75#137×C139—41no—
76AGL(1,ℤ/8)×C139—22no—
77AGL(1,ℤ/8)×C139—41no—
78#135×C139—42no—
79C2×M16×C139—21no—
80C4⋊Q8×C139—21no—
81#127×C139D411yescharacteristic, complemented
82#127×C139C2311yescharacteristic
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#125×C139—21no—
90#125×C139—21no—
91#125×C139—21no—
92#124×C139—21no—
93#124×C139—21no—
94#124×C139—21no—
95#124×C139—21no—
96#124×C139D411yescharacteristic, complemented
97#124×C139C2311yescharacteristic
98#123×C139—21no—
99#123×C139—21no—
100#123×C139—21no—
101#123×C139—21no—
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—22no—
111#123×C139—22no—
112#123×C139—22no—
113#123×C139—41no—
114#123×C139—42no—
115#123×C139D411yescharacteristic
116#123×C139D411yescharacteristic, complemented
117#123×C139D411yescharacteristic, complemented
118#123×C139C2311yescharacteristic
119#123×C139C2311yescharacteristic
120#123×C139C2311yescharacteristic
121C22⋊Q8×C139—21no—
122C22⋊Q8×C139—21no—
123C22⋊Q8×C139—21no—
124C22⋊Q8×C139—21no—
125C22⋊Q8×C139—21no—
126C22⋊Q8×C139—21no—
127C22⋊Q8×C139—21no—
128C22⋊Q8×C139—21no—
129#121×C139—21no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139—21no—
133#121×C139—21no—
134#121×C139—21no—
135#121×C139—21no—
136#121×C139—21no—
137#121×C139—21no—
138#121×C139—21no—
139#121×C139—21no—
140#121×C139—21no—
141#121×C139—42no—
142#120×C139—21no—
143#120×C139—21no—
144#120×C139—21no—
145#120×C139—21no—
146#120×C139—22no—
147#120×C139—41no—
148#120×C139D411yescharacteristic
149#120×C139C2311yescharacteristic
150C4×Q8×C139—21no—
151C4×D4×C139—21no—
152C4×D4×C139—21no—
153C4×D4×C139—21no—
154C4×D4×C139—21no—
155C4×D4×C139—21no—
156C4×D4×C139—21no—
157C4×D4×C139—21no—
158C4×D4×C139—21no—
159C4×D4×C139—21no—
160#117×C139—21no—
161#117×C139—21no—
162#117×C139—21no—
163#117×C139D411yescharacteristic, complemented
164C2×C4⋊C4×C139—21no—
165C2×C4⋊C4×C139—21no—
166C2×C4⋊C4×C139—41no—
167C2×C22⋊C4×C139—21no—
168C2×C22⋊C4×C139—21no—
169C2×C22⋊C4×C139—21no—
170C2×C22⋊C4×C139—21no—
171C2×C22⋊C4×C139—41no—
172C2×C22⋊C4×C139D411yescharacteristic
173C2×C22⋊C4×C139D411yescharacteristic, complemented
174#104×C139—22no—
175#104×C139—22no—
176#100×C139—21no—
177#100×C139C2312yes—
178#99×C139—21no—
179#99×C139—21no—
180#99×C139—22no—
181#99×C139—22no—
182#99×C139—22no—
183#99×C139—22no—
184#99×C139C2312yes—
185#99×C139C2312yes—
186C24×C139—21no—
187C24×C139—21no—
188C24×C139C2×D411yescharacteristic
189C24×C139C2×D411yescharacteristic
190C24×C139C2×D411yescharacteristic
191#41×C139—22no—
192#41×C139—22no—
193#41×C139—42no—
194#41×C139—41no—
195#41×C139—42no—
196#41×C139—42no—
197#41×C139—41no—
198#41×C139—41no—
199#41×C139—42no—
200#41×C139—41no—
201#41×C139—81no—
202#41×C139—81no—
203C2×Q8×C139—21no—
204C2×Q8×C139—21no—
205C2×Q8×C139—21no—
206C2×Q8×C139C2×D411yescharacteristic
207C2×D4×C139—21no—
208C2×D4×C139—22no—
209C2×D4×C139—22no—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—22no—
213C2×D4×C139—22no—
214C2×D4×C139—21no—
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—41no—
224C2×D4×C139—41no—
225C2×D4×C139—42no—
226C2×D4×C139—42no—
227C2×D4×C139—41no—
228C2×D4×C139—41no—
229C2×D4×C139—41no—
230C2×D4×C139—41no—
231C2×D4×C139—42no—
232C2×D4×C139—42no—
233C2×D4×C139—41no—
234C2×D4×C139—41no—
235C2×D4×C139—41no—
236C2×D4×C139—41no—
237C2×D4×C139—41no—
238C2×D4×C139—42no—
239C2×D4×C139C2×D411yescharacteristic
240C2×D4×C139C2×D411yescharacteristic
241C2×D4×C139C2×D411yescharacteristic
242C2×D4×C139C2×D411yescharacteristic
243C2×D4×C139C2411yescharacteristic
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—21no—
249C22×C4×C139—21no—
250C22×C4×C139—21no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—41no—
256C22×C4×C139—41no—
257C22×C4×C139—41no—
258C22×C4×C139—41no—
259C22×C4×C139—41no—
260C22×C4×C139C2×D411yescharacteristic
261C22×C4×C139C2×D411yescharacteristic
262C22×C4×C139C2×D411yescharacteristic
263C22×C4×C139C2×D411yescharacteristic
264Q16×C139—42no—
265SD16×C139—42no—
266SD16×C139—42no—
267D8×C139—42no—
268M16×C139—22no—
269M16×C139—41no—
270C2×C8×C139—41no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139—21no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139—21no—
289C4⋊C4×C139—21no—
290C4⋊C4×C139—42no—
291C4⋊C4×C139—42no—
292C4⋊C4×C139—42no—
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—21no—
312C22⋊C4×C139—21no—
313C22⋊C4×C139—21no—
314C22⋊C4×C139—21no—
315C22⋊C4×C139—21no—
316C22⋊C4×C139—22no—
317C22⋊C4×C139—22no—
318C22⋊C4×C139—42no—
319C22⋊C4×C139—41no—
320C22⋊C4×C139—41no—
321C22⋊C4×C139—42no—
322C22⋊C4×C139—42no—
323C22⋊C4×C139—42no—
324C22⋊C4×C139C2×D411yescharacteristic
325C22⋊C4×C139C2×D411yescharacteristic
326C22⋊C4×C139C2×D411yescharacteristic
327C22⋊C4×C139C2×D411yescharacteristic
328C42×C139—21no—
329C42×C139—21no—
330C42×C139—21no—
331C42×C139—21no—
332C42×C139C2×D411yescharacteristic
333C42×C139C2×D411yescharacteristic
334C23×C139—21no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—22no—
339C23×C139—22no—
340C23×C139—21no—
341C23×C139—21no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—81no—
347C23×C139—81no—
348C23×C139—81no—
349C23×C139—82no—
350C23×C139—161no—
351C23×C139#12011yescharacteristic
352C23×C139#12011yescharacteristic
353C23×C139#12011yescharacteristic
354C23×C139C22×D411yescharacteristic
355C23×C139C22×D411yescharacteristic
356Q8×C139—22no—
357Q8×C139—41no—
358Q8×C139—41no—
359Q8×C139—81no—
360Q8×C139—81no—
361D4×C139—22no—
362D4×C139—41no—
363D4×C139—41no—
364D4×C139—41no—
365D4×C139—41no—
366D4×C139—41no—
367D4×C139—41no—
368D4×C139—42no—
369D4×C139—42no—
370D4×C139—42no—
371D4×C139—42no—
372D4×C139—42no—
373D4×C139—42no—
374D4×C139—41no—
375D4×C139—41no—
376D4×C139—41no—
377D4×C139—41no—
378D4×C139—81no—
379D4×C139—81no—
380D4×C139—81no—
381D4×C139—81no—
382D4×C139—81no—
383D4×C139—81no—
384D4×C139—81no—
385D4×C139—81no—
386D4×C139—81no—
387D4×C139—162no—
388C2×C4×C139—21no—
389C2×C4×C139—21no—
390C2×C4×C139—22no—
391C2×C4×C139—22no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—21no—
395C2×C4×C139—21no—
396C2×C4×C139—21no—
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—21no—
402C2×C4×C139—42no—
403C2×C4×C139—42no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139—41no—
409C2×C4×C139—41no—
410C2×C4×C139—41no—
411C2×C4×C139—41no—
412C2×C4×C139—42no—
413C2×C4×C139—42no—
414C2×C4×C139—81no—
415C2×C4×C139—81no—
416C2×C4×C139—81no—
417C2×C4×C139—81no—
418C2×C4×C139—81no—
419C2×C4×C139—81no—
420C2×C4×C139—81no—
421C2×C4×C139—81no—
422C2×C4×C139—82no—
423C2×C4×C139—161no—
424C2×C4×C139#12011yescharacteristic
425C2×C4×C139C22×D411yescharacteristic
426C8×C139—42no—
427C22×C139—21no—
428C22×C139—21no—
429C22×C139—21no—
430C22×C139—21no—
431C22×C139—41no—
432C22×C139—41no—
433C22×C139—41no—
434C22×C139—41no—
435C22×C139—41no—
436C22×C139—42no—
437C22×C139—41no—
438C22×C139—41no—
439C22×C139—41no—
440C22×C139—41no—
441C22×C139—42no—
442C22×C139—41no—
443C22×C139—41no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139—81no—
447C22×C139—82no—
448C22×C139—82no—
449C22×C139—82no—
450C22×C139—82no—
451C22×C139—161no—
452C22×C139—161no—
453C22×C139B(4,𝔽2)11yescharacteristic
454C22×C139B(4,𝔽2)11yescharacteristic
455C22×C139C2×#12011yescharacteristic
456C4×C139—21no—
457C4×C139—21no—
458C4×C139—41no—
459C4×C139—41no—
460C4×C139—41no—
461C4×C139—41no—
462C4×C139—41no—
463C4×C139—41no—
464C4×C139—42no—
465C4×C139—41no—
466C4×C139—41no—
467C4×C139—41no—
468C4×C139—41no—
469C4×C139—82no—
470C4×C139—82no—
471C2×C139—21no—
472C2×C139—21no—
473C2×C139—21no—
474C2×C139—41no—
475C2×C139—41no—
476C2×C139—41no—
477C2×C139—41no—
478C2×C139—81no—
479C2×C139—81no—
480C2×C139—82no—
481C2×C139C2×B(4,𝔽2)11yescharacteristic
482#33552C13911yesmaximal, characteristic, direct product factor, Sylow
483C139#3355211yescharacteristic, direct product factor, Sylow
484#3533C2×C13911yescharacteristic, complemented
485#3026C2×C13911yescharacteristic, complemented
486C2×#458C2×C13911yescharacteristic, complemented
487#3019C2×C13911yescharacteristic, complemented
488#2201C2×C13912yescomplemented
489#2200C2×C13912yescomplemented
490#2198C2×C13912yescomplemented
491#2197C2×C13912yescomplemented
492#2127C2×C13911yescharacteristic, complemented
493#2121C2×C13911yescharacteristic, complemented
494C2×#352C2×C13911yescharacteristic, complemented
495C2×H(5,𝔽2)C22×C13911yescharacteristic
496#575—21no—
497#563C22×C13911yescharacteristic, complemented
498#562—21no—
499#560C22×C13911yescharacteristic, complemented
500#559C22×C13911yescharacteristic, complemented
501#553—21no—
502#552—21no—
503#551—21no—
504#551C22×C13911yescharacteristic, complemented
505#547—21no—
506#546—21no—
507#542—21no—
508#540—21no—
509#539—21no—
510#538—21no—
511#538—21no—
512#535C22×C13911yescharacteristic
513#534—21no—
514#534C22×C13911yescharacteristic
515#525—21no—
516C2×#123—21no—
517C2×#123C22×C13911yescharacteristic
518#458—21no—
519#458—21no—
520#458—21no—
521#458C22×C13912yes—
522#458C22×C13912yes—
523#458C22×C13912yes—
524B(4,𝔽2)—21no—
525B(4,𝔽2)C22×C13912yes—
526#455—21no—
527#455C22×C13912yes—
528#453—21no—
529#453C22×C13912yes—
530#421—21no—
531C2×#100C22×C13911yescharacteristic
532C2×#99—21no—
533C2×#99—21no—
534C2×#99C22×C13911yescharacteristic
535C2×#99C22×C13911yescharacteristic
536#354C22×C13912yescomplemented
537#353C22×C13912yescomplemented
538#352C22×C13912yescomplemented
539#352C22×C13912yescomplemented
540#352C22×C13912yescomplemented
541AΣL(1,𝔽16)C22×C13912yescomplemented
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C13912yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C13911yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C13911yescharacteristic
555C22×D4C23×C13911yescharacteristic
556C23×C4D4×C13911yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C13911yescharacteristic, complemented
565#127C23×C13911yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C13911yescharacteristic, complemented
580#124C23×C13911yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C13911yescharacteristic
599#123D4×C13911yescharacteristic, complemented
600#123D4×C13911yescharacteristic, complemented
601#123C23×C13911yescharacteristic
602#123C23×C13911yescharacteristic
603#123C23×C13911yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C13911yescharacteristic
632#120C23×C13911yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C13911yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C13911yescharacteristic
656C2×C22⋊C4D4×C13911yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C13912yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C13912yes—
668#99C23×C13912yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C13911yescharacteristic
672C24C2×D4×C13911yescharacteristic
673C24C2×D4×C13911yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C13911yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C13911yescharacteristic
723C2×D4C2×D4×C13911yescharacteristic
724C2×D4C2×D4×C13911yescharacteristic
725C2×D4C2×D4×C13911yescharacteristic
726C2×D4C24×C13911yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C13911yescharacteristic
744C22×C4C2×D4×C13911yescharacteristic
745C22×C4C2×D4×C13911yescharacteristic
746C22×C4C2×D4×C13911yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C13911yescharacteristic
808C22⋊C4C2×D4×C13911yescharacteristic
809C22⋊C4C2×D4×C13911yescharacteristic
810C22⋊C4C2×D4×C13911yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C13911yescharacteristic
816C42C2×D4×C13911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C13911yescharacteristic
835C23#120×C13911yescharacteristic
836C23#120×C13911yescharacteristic
837C23C22×D4×C13911yescharacteristic
838C23C22×D4×C13911yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C13911yescharacteristic
908C2×C4C22×D4×C13911yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22B(4,𝔽2)×C13911yescharacteristic
937C22B(4,𝔽2)×C13911yescharacteristic
938C22C2×#120×C13911yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×B(4,𝔽2)×C13911yescharacteristic
subgroupG/H
center, socleC2×C139C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C139
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3533×C139C2semidirect
2. #3026×C139C2semidirect
3. C2×#458×C139C2semidirect
4. #3019×C139C2semidirect
5. #2201×C139C2semidirect
6. #2200×C139C2semidirect
7. #2198×C139C2semidirect
8. #2197×C139C2semidirect
9. #2127×C139C2semidirect
10. #2121×C139C2semidirect
11. C2×#352×C139C2semidirect
14. #563×C139C22semidirect
16. #560×C139C22semidirect
17. #559×C139C22semidirect
21. #551×C139C22semidirect
53. #354×C139C22semidirect
54. #353×C139C22semidirect
55. #352×C139C22semidirect
56. #352×C139C22semidirect
57. #352×C139C22semidirect
58. AΣL(1,𝔽16)×C139C22semidirect
67. C2×#41×C139D4semidirect
73. C23×C4×C139D4semidirect
81. #127×C139D4semidirect
96. #124×C139D4semidirect
116. #123×C139D4semidirect
117. #123×C139D4semidirect
163. #117×C139D4semidirect
173. C2×C22⋊C4×C139D4semidirect
482. #33552C139direct (N × H)
483. C139#33552direct (N × H)
484. #3533C2×C139semidirect
485. #3026C2×C139semidirect
486. C2×#458C2×C139semidirect
487. #3019C2×C139semidirect
488. #2201C2×C139semidirect
489. #2200C2×C139semidirect
490. #2198C2×C139semidirect
491. #2197C2×C139semidirect
492. #2127C2×C139semidirect
493. #2121C2×C139semidirect
494. C2×#352C2×C139semidirect
497. #563C22×C139semidirect
499. #560C22×C139semidirect
500. #559C22×C139semidirect
504. #551C22×C139semidirect
536. #354C22×C139semidirect
537. #353C22×C139semidirect
538. #352C22×C139semidirect
539. #352C22×C139semidirect
540. #352C22×C139semidirect
541. AΣL(1,𝔽16)C22×C139semidirect
550. C2×#41D4×C139semidirect
556. C23×C4D4×C139semidirect
564. #127D4×C139semidirect
579. #124D4×C139semidirect
599. #123D4×C139semidirect
600. #123D4×C139semidirect
646. #117D4×C139semidirect
656. C2×C22⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3533×C1392
#3026×C1392
C2×#458×C1392
#3019×C1392
#2201×C1392
#2200×C1392
#2198×C1392
#2197×C1392
#2127×C1392
#2121×C1392
C2×#352×C1392
#33552139