Finite Group Databasebeta

← C139×#33551 #48028147

Subgroups — C139×#33551 #48028147

Order 35584.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3532×C139C211yesmaximal, characteristic, complemented
2#3026×C139C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C139C211yesmaximal, characteristic, complemented
4#3019×C139C211yesmaximal, characteristic, complemented
5#2200×C139C212yesmaximal, complemented
6#2199×C139C212yesmaximal, complemented
7#2197×C139C212yesmaximal, complemented
8#2196×C139C212yesmaximal, complemented
9#2127×C139C211yesmaximal, characteristic, complemented
10#2121×C139C211yesmaximal, characteristic, complemented
11C2×AΣL(1,𝔽16)×C139C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C139C2211yescharacteristic, complemented
13#575×C139—21no—
14H(3,𝔽4)×C139C2211yescharacteristic, complemented
15#560×C139—21no—
16#560×C139C2211yescharacteristic, complemented
17#551×C139—21no—
18#551×C139C2211yescharacteristic, complemented
19#546×C139—21no—
20#546×C139—21no—
21#546×C139—21no—
22D42×C139—21no—
23D42×C139C2211yescharacteristic, complemented
24#538×C139—21no—
25#538×C139—21no—
26#538×C139—21no—
27#535×C139—21no—
28#535×C139C2211yescharacteristic
29#534×C139—21no—
30#534×C139—21no—
31#534×C139C2211yescharacteristic
32C2×#120×C139—21no—
33C2×#120×C139—21no—
34C2×#120×C139C2211yescharacteristic
35#458×C139—21no—
36#458×C139C2212yescomplemented
37B(4,𝔽2)×C139—21no—
38B(4,𝔽2)×C139—21no—
39B(4,𝔽2)×C139—21no—
40B(4,𝔽2)×C139C2212yes—
41B(4,𝔽2)×C139C2212yescomplemented
42B(4,𝔽2)×C139C2212yescomplemented
43#455×C139—21no—
44#455×C139C2212yescomplemented
45#453×C139—21no—
46#453×C139C2212yescomplemented
47#421×C139—21no—
48C2×#100×C139C2211yescharacteristic, complemented
49C2×#99×C139—21no—
50C2×#99×C139—21no—
51C2×#99×C139C2211yescharacteristic, complemented
52C2×#99×C139C2211yescharacteristic, complemented
53#354×C139C2212yescomplemented
54#353×C139C2212yescomplemented
55#352×C139C2212yescomplemented
56AΣL(1,𝔽16)×C139C2212yescomplemented
57AΣL(1,𝔽16)×C139C2212yescomplemented
58AΣL(1,𝔽16)×C139C2212yescomplemented
59C25×C139D411yescharacteristic, complemented
60H(5,𝔽2)×C139—21no—
61H(5,𝔽2)×C139—21no—
62H(5,𝔽2)×C139—21no—
63H(5,𝔽2)×C139—42no—
64H(5,𝔽2)×C139C2312yes—
65C2×#41×C139—21no—
66C2×#41×C139—21no—
67C2×#41×C139—41no—
68C2×#41×C139D411yescharacteristic, complemented
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—41no—
77C22×D4×C139—41no—
78C22×D4×C139D411yescharacteristic, complemented
79C22×D4×C139C2311yescharacteristic
80#137×C139—22no—
81#137×C139—41no—
82AGL(1,ℤ/8)×C139—22no—
83AGL(1,ℤ/8)×C139—41no—
84#135×C139—42no—
85C2×M16×C139—21no—
86#127×C139—21no—
87#127×C139D411yescharacteristic, complemented
88#127×C139C2311yescharacteristic
89#126×C139—21no—
90#126×C139—21no—
91#126×C139—21no—
92#126×C139—21no—
93#124×C139—21no—
94#124×C139—21no—
95#124×C139—21no—
96#124×C139—21no—
97#124×C139—21no—
98#124×C139D411yescharacteristic, complemented
99#124×C139C2311yescharacteristic
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—22no—
109#123×C139—41no—
110#123×C139D411yescharacteristic, complemented
111#123×C139C2311yescharacteristic
112C22⋊Q8×C139—21no—
113C22⋊Q8×C139—21no—
114C22⋊Q8×C139—21no—
115#121×C139—21no—
116#121×C139—21no—
117#121×C139—21no—
118#121×C139—21no—
119#121×C139—21no—
120#121×C139—21no—
121#121×C139—21no—
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—42no—
131#120×C139—21no—
132#120×C139—21no—
133#120×C139—21no—
134#120×C139—21no—
135#120×C139—21no—
136#120×C139—21no—
137#120×C139—21no—
138#120×C139—21no—
139#120×C139—21no—
140#120×C139—21no—
141#120×C139—21no—
142#120×C139—21no—
143#120×C139—21no—
144#120×C139—21no—
145#120×C139—22no—
146#120×C139—22no—
147#120×C139—22no—
148#120×C139—42no—
149#120×C139—41no—
150#120×C139D411yescharacteristic, complemented
151#120×C139D411yescharacteristic, complemented
152#120×C139D411yescharacteristic, complemented
153#120×C139C2311yescharacteristic
154#120×C139C2311yescharacteristic
155#120×C139C2311yescharacteristic
156C4×D4×C139—21no—
157C4×D4×C139—21no—
158C4×D4×C139—21no—
159C4×D4×C139—21no—
160C4×D4×C139—21no—
161C4×D4×C139—21no—
162#117×C139—21no—
163#117×C139D411yescharacteristic, complemented
164C2×C22⋊C4×C139—21no—
165C2×C22⋊C4×C139—21no—
166C2×C22⋊C4×C139—21no—
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, complemented
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×C139—21no—
189C24×C139—21no—
190C24×C139—21no—
191C24×C139—41no—
192C24×C139—41no—
193C24×C139—82no—
194C24×C139C2×D411yescharacteristic
195C24×C139C2×D411yescharacteristic
196C24×C139C2×D411yescharacteristic
197C24×C139C2×D411yescharacteristic
198C24×C139C2×D411yescharacteristic, complemented
199#41×C139—22no—
200#41×C139—22no—
201#41×C139—42no—
202#41×C139—41no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—41no—
206#41×C139—41no—
207#41×C139—42no—
208#41×C139—41no—
209#41×C139—82no—
210C2×Q8×C139—21no—
211C2×Q8×C139—21no—
212C2×Q8×C139C2×D411yescharacteristic, complemented
213C2×D4×C139—21no—
214C2×D4×C139—21no—
215C2×D4×C139—21no—
216C2×D4×C139—22no—
217C2×D4×C139—22no—
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—22no—
222C2×D4×C139—22no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—21no—
229C2×D4×C139—21no—
230C2×D4×C139—21no—
231C2×D4×C139—21no—
232C2×D4×C139—21no—
233C2×D4×C139—21no—
234C2×D4×C139—21no—
235C2×D4×C139—21no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—41no—
239C2×D4×C139—41no—
240C2×D4×C139—42no—
241C2×D4×C139—42no—
242C2×D4×C139—41no—
243C2×D4×C139—41no—
244C2×D4×C139—41no—
245C2×D4×C139—41no—
246C2×D4×C139—42no—
247C2×D4×C139—42no—
248C2×D4×C139—41no—
249C2×D4×C139—41no—
250C2×D4×C139—41no—
251C2×D4×C139—41no—
252C2×D4×C139—41no—
253C2×D4×C139—42no—
254C2×D4×C139—42no—
255C2×D4×C139—42no—
256C2×D4×C139—82no—
257C2×D4×C139—82no—
258C2×D4×C139—82no—
259C2×D4×C139—82no—
260C2×D4×C139—81no—
261C2×D4×C139—81no—
262C2×D4×C139—84no—
263C2×D4×C139C2×D411yescharacteristic
264C2×D4×C139C2×D411yescharacteristic
265C2×D4×C139C2×D411yescharacteristic
266C2×D4×C139C2×D411yescharacteristic, complemented
267C2×D4×C139C2411yescharacteristic
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—21no—
275C22×C4×C139—21no—
276C22×C4×C139—21no—
277C22×C4×C139—21no—
278C22×C4×C139—41no—
279C22×C4×C139—41no—
280C22×C4×C139—41no—
281C22×C4×C139C2×D411yescharacteristic
282C22×C4×C139C2×D411yescharacteristic, complemented
283Q16×C139—42no—
284SD16×C139—42no—
285SD16×C139—42no—
286D8×C139—42no—
287M16×C139—22no—
288M16×C139—41no—
289C2×C8×C139—41no—
290C4⋊C4×C139—21no—
291C4⋊C4×C139—21no—
292C4⋊C4×C139—21no—
293C4⋊C4×C139—21no—
294C4⋊C4×C139—21no—
295C4⋊C4×C139—21no—
296C4⋊C4×C139—21no—
297C4⋊C4×C139—21no—
298C4⋊C4×C139—21no—
299C4⋊C4×C139—42no—
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—21no—
317C22⋊C4×C139—21no—
318C22⋊C4×C139—21no—
319C22⋊C4×C139—21no—
320C22⋊C4×C139—21no—
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—42no—
328C22⋊C4×C139—42no—
329C22⋊C4×C139—42no—
330C22⋊C4×C139—41no—
331C22⋊C4×C139—41no—
332C22⋊C4×C139—42no—
333C22⋊C4×C139C2×D411yescharacteristic
334C22⋊C4×C139C2×D411yescharacteristic
335C22⋊C4×C139C2×D411yescharacteristic, complemented
336C22⋊C4×C139C2×D411yescharacteristic, complemented
337C42×C139—21no—
338C42×C139—21no—
339C42×C139C2×D411yescharacteristic, complemented
340C42×C139C2×D411yescharacteristic, complemented
341C23×C139—21no—
342C23×C139—21no—
343C23×C139—21no—
344C23×C139—21no—
345C23×C139—21no—
346C23×C139—22no—
347C23×C139—22no—
348C23×C139—21no—
349C23×C139—21no—
350C23×C139—21no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—42no—
354C23×C139—42no—
355C23×C139—42no—
356C23×C139—41no—
357C23×C139—41no—
358C23×C139—42no—
359C23×C139—41no—
360C23×C139—44no—
361C23×C139—41no—
362C23×C139—41no—
363C23×C139—41no—
364C23×C139—81no—
365C23×C139—81no—
366C23×C139—81no—
367C23×C139—81no—
368C23×C139—81no—
369C23×C139—81no—
370C23×C139—81no—
371C23×C139—81no—
372C23×C139—81no—
373C23×C139—82no—
374C23×C139—82no—
375C23×C139—82no—
376C23×C139—82no—
377C23×C139—161no—
378C23×C139#12011yescharacteristic
379C23×C139#12011yescharacteristic
380C23×C139#12011yescharacteristic
381C23×C139C22×D411yescharacteristic
382C23×C139C22×D411yescharacteristic
383Q8×C139—22no—
384Q8×C139—41no—
385Q8×C139—41no—
386Q8×C139—81no—
387D4×C139—22no—
388D4×C139—41no—
389D4×C139—41no—
390D4×C139—41no—
391D4×C139—41no—
392D4×C139—41no—
393D4×C139—41no—
394D4×C139—42no—
395D4×C139—42no—
396D4×C139—42no—
397D4×C139—42no—
398D4×C139—42no—
399D4×C139—42no—
400D4×C139—42no—
401D4×C139—42no—
402D4×C139—42no—
403D4×C139—42no—
404D4×C139—41no—
405D4×C139—41no—
406D4×C139—41no—
407D4×C139—41no—
408D4×C139—81no—
409D4×C139—81no—
410D4×C139—81no—
411D4×C139—81no—
412D4×C139—81no—
413D4×C139—81no—
414D4×C139—81no—
415D4×C139—81no—
416D4×C139—81no—
417D4×C139—81no—
418D4×C139—81no—
419D4×C139—81no—
420D4×C139—81no—
421D4×C139—81no—
422D4×C139—84no—
423D4×C139—84no—
424D4×C139—162no—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—22no—
428C2×C4×C139—22no—
429C2×C4×C139—21no—
430C2×C4×C139—21no—
431C2×C4×C139—21no—
432C2×C4×C139—21no—
433C2×C4×C139—21no—
434C2×C4×C139—21no—
435C2×C4×C139—21no—
436C2×C4×C139—21no—
437C2×C4×C139—42no—
438C2×C4×C139—42no—
439C2×C4×C139—41no—
440C2×C4×C139—41no—
441C2×C4×C139—42no—
442C2×C4×C139—41no—
443C2×C4×C139—41no—
444C2×C4×C139—42no—
445C2×C4×C139—42no—
446C2×C4×C139—81no—
447C2×C4×C139—81no—
448C2×C4×C139—81no—
449C2×C4×C139—81no—
450C2×C4×C139—81no—
451C2×C4×C139—81no—
452C2×C4×C139—81no—
453C2×C4×C139—82no—
454C2×C4×C139—161no—
455C2×C4×C139#12011yescharacteristic
456C2×C4×C139C22×D411yescharacteristic
457C8×C139—42no—
458C22×C139—22no—
459C22×C139—21no—
460C22×C139—21no—
461C22×C139—21no—
462C22×C139—21no—
463C22×C139—41no—
464C22×C139—41no—
465C22×C139—41no—
466C22×C139—41no—
467C22×C139—41no—
468C22×C139—41no—
469C22×C139—42no—
470C22×C139—41no—
471C22×C139—41no—
472C22×C139—41no—
473C22×C139—41no—
474C22×C139—41no—
475C22×C139—41no—
476C22×C139—42no—
477C22×C139—41no—
478C22×C139—42no—
479C22×C139—42no—
480C22×C139—41no—
481C22×C139—41no—
482C22×C139—41no—
483C22×C139—81no—
484C22×C139—81no—
485C22×C139—81no—
486C22×C139—82no—
487C22×C139—82no—
488C22×C139—82no—
489C22×C139—81no—
490C22×C139—84no—
491C22×C139—82no—
492C22×C139—82no—
493C22×C139—82no—
494C22×C139—81no—
495C22×C139—162no—
496C22×C139—161no—
497C22×C139—161no—
498C22×C139B(4,𝔽2)11yescharacteristic
499C22×C139B(4,𝔽2)11yescharacteristic
500C22×C139C2×#12011yescharacteristic
501C4×C139—21no—
502C4×C139—21no—
503C4×C139—41no—
504C4×C139—41no—
505C4×C139—41no—
506C4×C139—41no—
507C4×C139—41no—
508C4×C139—41no—
509C4×C139—42no—
510C4×C139—41no—
511C4×C139—41no—
512C4×C139—82no—
513C4×C139—82no—
514C2×C139—21no—
515C2×C139—21no—
516C2×C139—21no—
517C2×C139—41no—
518C2×C139—41no—
519C2×C139—42no—
520C2×C139—41no—
521C2×C139—41no—
522C2×C139—81no—
523C2×C139—81no—
524C2×C139—81no—
525C2×C139—82no—
526C2×C139C2×B(4,𝔽2)11yescharacteristic
527#33551C13911yesmaximal, characteristic, direct product factor, Sylow
528C139#3355111yescharacteristic, direct product factor, Sylow
529#3532C2×C13911yescharacteristic, complemented
530#3026C2×C13911yescharacteristic, complemented
531C2×B(4,𝔽2)C2×C13911yescharacteristic, complemented
532#3019C2×C13911yescharacteristic, complemented
533#2200C2×C13912yescomplemented
534#2199C2×C13912yescomplemented
535#2197C2×C13912yescomplemented
536#2196C2×C13912yescomplemented
537#2127C2×C13911yescharacteristic, complemented
538#2121C2×C13911yescharacteristic, complemented
539C2×AΣL(1,𝔽16)C2×C13911yescharacteristic, complemented
540C2×H(5,𝔽2)C22×C13911yescharacteristic, complemented
541#575—21no—
542H(3,𝔽4)C22×C13911yescharacteristic, complemented
543#560—21no—
544#560C22×C13911yescharacteristic, complemented
545#551—21no—
546#551C22×C13911yescharacteristic, complemented
547#546—21no—
548#546—21no—
549#546—21no—
550D42—21no—
551D42C22×C13911yescharacteristic, complemented
552#538—21no—
553#538—21no—
554#538—21no—
555#535—21no—
556#535C22×C13911yescharacteristic
557#534—21no—
558#534—21no—
559#534C22×C13911yescharacteristic
560C2×#120—21no—
561C2×#120—21no—
562C2×#120C22×C13911yescharacteristic
563#458—21no—
564#458C22×C13912yescomplemented
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)—21no—
568B(4,𝔽2)C22×C13912yes—
569B(4,𝔽2)C22×C13912yescomplemented
570B(4,𝔽2)C22×C13912yescomplemented
571#455—21no—
572#455C22×C13912yescomplemented
573#453—21no—
574#453C22×C13912yescomplemented
575#421—21no—
576C2×#100C22×C13911yescharacteristic, complemented
577C2×#99—21no—
578C2×#99—21no—
579C2×#99C22×C13911yescharacteristic, complemented
580C2×#99C22×C13911yescharacteristic, complemented
581#354C22×C13912yescomplemented
582#353C22×C13912yescomplemented
583#352C22×C13912yescomplemented
584AΣL(1,𝔽16)C22×C13912yescomplemented
585AΣL(1,𝔽16)C22×C13912yescomplemented
586AΣL(1,𝔽16)C22×C13912yescomplemented
587C25D4×C13911yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C13912yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C13911yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C13911yescharacteristic, complemented
607C22×D4C23×C13911yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C13911yescharacteristic, complemented
616#127C23×C13911yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C13911yescharacteristic, complemented
627#124C23×C13911yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C13911yescharacteristic, complemented
639#123C23×C13911yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C13911yescharacteristic, complemented
679#120D4×C13911yescharacteristic, complemented
680#120D4×C13911yescharacteristic, complemented
681#120C23×C13911yescharacteristic
682#120C23×C13911yescharacteristic
683#120C23×C13911yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C13911yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C13911yescharacteristic, complemented
701C2×C22⋊C4D4×C13911yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C13912yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C13912yes—
713#99C23×C13912yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C13911yescharacteristic
723C24C2×D4×C13911yescharacteristic
724C24C2×D4×C13911yescharacteristic
725C24C2×D4×C13911yescharacteristic
726C24C2×D4×C13911yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C13911yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C13911yescharacteristic
792C2×D4C2×D4×C13911yescharacteristic
793C2×D4C2×D4×C13911yescharacteristic
794C2×D4C2×D4×C13911yescharacteristic, complemented
795C2×D4C24×C13911yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C13911yescharacteristic
810C22×C4C2×D4×C13911yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C13911yescharacteristic
862C22⋊C4C2×D4×C13911yescharacteristic
863C22⋊C4C2×D4×C13911yescharacteristic, complemented
864C22⋊C4C2×D4×C13911yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C13911yescharacteristic, complemented
868C42C2×D4×C13911yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C13911yescharacteristic
907C23#120×C13911yescharacteristic
908C23#120×C13911yescharacteristic
909C23C22×D4×C13911yescharacteristic
910C23C22×D4×C13911yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C13911yescharacteristic
984C2×C4C22×D4×C13911yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22B(4,𝔽2)×C13911yescharacteristic
1027C22B(4,𝔽2)×C13911yescharacteristic
1028C22C2×#120×C13911yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×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. #3532×C139C2semidirect
2. #3026×C139C2semidirect
3. C2×B(4,𝔽2)×C139C2semidirect
4. #3019×C139C2semidirect
5. #2200×C139C2semidirect
6. #2199×C139C2semidirect
7. #2197×C139C2semidirect
8. #2196×C139C2semidirect
9. #2127×C139C2semidirect
10. #2121×C139C2semidirect
11. C2×AΣL(1,𝔽16)×C139C2semidirect
12. C2×H(5,𝔽2)×C139C22semidirect
14. H(3,𝔽4)×C139C22semidirect
16. #560×C139C22semidirect
18. #551×C139C22semidirect
23. D42×C139C22semidirect
36. #458×C139C22semidirect
41. B(4,𝔽2)×C139C22semidirect
42. B(4,𝔽2)×C139C22semidirect
44. #455×C139C22semidirect
46. #453×C139C22semidirect
48. C2×#100×C139C22semidirect
51. C2×#99×C139C22semidirect
52. C2×#99×C139C22semidirect
53. #354×C139C22semidirect
54. #353×C139C22semidirect
55. #352×C139C22semidirect
56. AΣL(1,𝔽16)×C139C22semidirect
57. AΣL(1,𝔽16)×C139C22semidirect
58. AΣL(1,𝔽16)×C139C22semidirect
59. C25×C139D4semidirect
68. C2×#41×C139D4semidirect
78. C22×D4×C139D4semidirect
87. #127×C139D4semidirect
98. #124×C139D4semidirect
110. #123×C139D4semidirect
150. #120×C139D4semidirect
151. #120×C139D4semidirect
152. #120×C139D4semidirect
163. #117×C139D4semidirect
172. C2×C22⋊C4×C139D4semidirect
173. C2×C22⋊C4×C139D4semidirect
198. C24×C139C2×D4semidirect
212. C2×Q8×C139C2×D4semidirect
266. C2×D4×C139C2×D4semidirect
282. C22×C4×C139C2×D4semidirect
335. C22⋊C4×C139C2×D4semidirect
336. C22⋊C4×C139C2×D4semidirect
339. C42×C139C2×D4semidirect
340. C42×C139C2×D4semidirect
527. #33551C139direct (N × H)
528. C139#33551direct (N × H)
529. #3532C2×C139semidirect
530. #3026C2×C139semidirect
531. C2×B(4,𝔽2)C2×C139semidirect
532. #3019C2×C139semidirect
533. #2200C2×C139semidirect
534. #2199C2×C139semidirect
535. #2197C2×C139semidirect
536. #2196C2×C139semidirect
537. #2127C2×C139semidirect
538. #2121C2×C139semidirect
539. C2×AΣL(1,𝔽16)C2×C139semidirect
540. C2×H(5,𝔽2)C22×C139semidirect
542. H(3,𝔽4)C22×C139semidirect
544. #560C22×C139semidirect
546. #551C22×C139semidirect
551. D42C22×C139semidirect
564. #458C22×C139semidirect
569. B(4,𝔽2)C22×C139semidirect
570. B(4,𝔽2)C22×C139semidirect
572. #455C22×C139semidirect
574. #453C22×C139semidirect
576. C2×#100C22×C139semidirect
579. C2×#99C22×C139semidirect
580. C2×#99C22×C139semidirect
581. #354C22×C139semidirect
582. #353C22×C139semidirect
583. #352C22×C139semidirect
584. AΣL(1,𝔽16)C22×C139semidirect
585. AΣL(1,𝔽16)C22×C139semidirect
586. AΣL(1,𝔽16)C22×C139semidirect
587. C25D4×C139semidirect
596. C2×#41D4×C139semidirect
606. C22×D4D4×C139semidirect
615. #127D4×C139semidirect
626. #124D4×C139semidirect
638. #123D4×C139semidirect
678. #120D4×C139semidirect
679. #120D4×C139semidirect
680. #120D4×C139semidirect
691. #117D4×C139semidirect
700. C2×C22⋊C4D4×C139semidirect
701. C2×C22⋊C4D4×C139semidirect
726. C24C2×D4×C139semidirect
740. C2×Q8C2×D4×C139semidirect
794. C2×D4C2×D4×C139semidirect
810. C22×C4C2×D4×C139semidirect
863. C22⋊C4C2×D4×C139semidirect
864. C22⋊C4C2×D4×C139semidirect
867. C42C2×D4×C139semidirect
868. C42C2×D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3532×C1392
#3026×C1392
C2×B(4,𝔽2)×C1392
#3019×C1392
#2200×C1392
#2199×C1392
#2197×C1392
#2196×C1392
#2127×C1392
#2121×C1392
C2×AΣL(1,𝔽16)×C1392
#33551139