Finite Group Databasebeta

← C139×#24402 #48018998

Subgroups — C139×#24402 #48018998

Order 35584.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic, complemented
2C2×#472×C139C211yesmaximal, characteristic, complemented
3C2×#471×C139C211yesmaximal, characteristic, complemented
4#3006×C139C211yesmaximal, characteristic, complemented
5C2×#449×C139C211yesmaximal, characteristic, complemented
6#2880×C139C211yesmaximal, characteristic, complemented
7#2052×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2019×C139C211yesmaximal, characteristic, complemented
10#2018×C139C211yesmaximal, characteristic, complemented
11#1908×C139C211yesmaximal, characteristic, complemented
12#1907×C139C211yesmaximal, characteristic, complemented
13#1900×C139C211yesmaximal, characteristic, complemented
14#1855×C139C211yesmaximal, characteristic, complemented
15#1785×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18#575×C139—24no—
19#575×C139—24no—
20C2×#137×C139—21no—
21C2×#137×C139C2211yescharacteristic
22C2×#137×C139C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C139—21no—
24C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
28C2×#135×C139—21no—
29C2×#135×C139—21no—
30C22×SD16×C139C2211yescharacteristic, complemented
31C22×D8×C139C2211yescharacteristic, complemented
32C2×#131×C139C2211yescharacteristic
33C2×#131×C139C2211yescharacteristic
34C22×M16×C139C2211yescharacteristic
35C2×#121×C139C2211yescharacteristic
36#472×C139—24no—
37#471×C139—24no—
38#449×C139—21no—
39#449×C139—21no—
40#449×C139—21no—
41#449×C139—21no—
42#449×C139—21no—
43#449×C139—21no—
44#448×C139—21no—
45#447×C139—21no—
46C2×#108×C139C2211yescharacteristic, complemented
47C2×#108×C139C2211yescharacteristic, complemented
48#417×C139C2211yescharacteristic
49#417×C139C2211yescharacteristic
50C2×#103×C139C2211yescharacteristic, complemented
51C2×#102×C139C2211yescharacteristic, complemented
52C2×#101×C139C2211yescharacteristic, complemented
53C2×#101×C139C2211yescharacteristic, complemented
54C2×#100×C139C2211yescharacteristic, complemented
55C2×#100×C139C2211yescharacteristic, complemented
56C2×#100×C139C2211yescharacteristic, complemented
57C2×#100×C139C2211yescharacteristic, complemented
58#408×C139—21no—
59#408×C139—21no—
60#408×C139C2211yescharacteristic
61#408×C139C2211yescharacteristic
62#407×C139—21no—
63#407×C139C2211yescharacteristic
64#407×C139C2211yescharacteristic
65C2×C22⋊C8×C139—21no—
66C2×C22⋊C8×C139C2211yescharacteristic
67#343×C139C2211yescharacteristic, complemented
68#343×C139C2211yescharacteristic, complemented
69#341×C139C2211yescharacteristic, complemented
70#341×C139C2211yescharacteristic, complemented
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—22no—
74C2×#41×C139—22no—
75C2×#41×C139—22no—
76C2×#41×C139—22no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—41no—
82C2×#41×C139—41no—
83C2×#41×C139—41no—
84C2×#41×C139—41no—
85C2×#41×C139D411yescharacteristic
86C2×#41×C139D411yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C22×Q8×C139D411yescharacteristic
90C22×Q8×C139C2311yescharacteristic
91C22×D4×C139—21no—
92C22×D4×C139—21no—
93C22×D4×C139—21no—
94C22×D4×C139D411yescharacteristic
95C22×D4×C139C2311yescharacteristic
96C22×D4×C139C2311yescharacteristic
97C23×C4×C139—21no—
98C23×C4×C139—21no—
99C23×C4×C139C2311yescharacteristic
100#137×C139—28no—
101#137×C139—22no—
102#137×C139—22no—
103#137×C139—22no—
104#137×C139D414yescomplemented
105AGL(1,ℤ/8)×C139—28no—
106AGL(1,ℤ/8)×C139—22no—
107AGL(1,ℤ/8)×C139—22no—
108AGL(1,ℤ/8)×C139—22no—
109AGL(1,ℤ/8)×C139—22no—
110AGL(1,ℤ/8)×C139—22no—
111AGL(1,ℤ/8)×C139—41no—
112AGL(1,ℤ/8)×C139—41no—
113AGL(1,ℤ/8)×C139D414yescomplemented
114#135×C139—28no—
115#135×C139—28no—
116C2×Q16×C139—21no—
117C2×Q16×C139—21no—
118C2×SD16×C139—21no—
119C2×SD16×C139—21no—
120C2×SD16×C139—21no—
121C2×SD16×C139—21no—
122C2×SD16×C139—21no—
123C2×SD16×C139—21no—
124C2×SD16×C139—22no—
125C2×SD16×C139—21no—
126C2×SD16×C139—21no—
127C2×SD16×C139—41no—
128C2×D8×C139—21no—
129C2×D8×C139—21no—
130C2×D8×C139—21no—
131C2×D8×C139—21no—
132C2×D8×C139—22no—
133C2×D8×C139—21no—
134C2×D8×C139—21no—
135C2×D8×C139—41no—
136#131×C139—22no—
137#131×C139—22no—
138#131×C139—41no—
139#131×C139—41no—
140C2×M16×C139—21no—
141C2×M16×C139—22no—
142C2×M16×C139—22no—
143C2×M16×C139—21no—
144C2×M16×C139—21no—
145C2×M16×C139C2311yescharacteristic
146C2×M16×C139C2311yescharacteristic
147C2×M16×C139C2311yescharacteristic
148C2×M16×C139C2311yescharacteristic
149C2×M16×C139C2311yescharacteristic
150C2×M16×C139C2311yescharacteristic
151C22×C8×C139—21no—
152C22×C8×C139—21no—
153C22×C8×C139—21no—
154C22×C8×C139C2311yescharacteristic
155C22×C8×C139C2311yescharacteristic
156#121×C139—21no—
157#121×C139—21no—
158#121×C139—21no—
159#121×C139—21no—
160C2×C4⋊C4×C139C2311yescharacteristic
161C2×C22⋊C4×C139—21no—
162#108×C139—22no—
163#108×C139—22no—
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—21no—
172#101×C139—22no—
173#101×C139—41no—
174#100×C139—22no—
175#100×C139—22no—
176#100×C139—22no—
177#100×C139—41no—
178C22⋊C8×C139—21no—
179C22⋊C8×C139—21no—
180C22⋊C8×C139—21no—
181C22⋊C8×C139—21no—
182C22⋊C8×C139—21no—
183C22⋊C8×C139—21no—
184C22⋊C8×C139—21no—
185C22⋊C8×C139—21no—
186C22⋊C8×C139D411yescharacteristic
187C22⋊C8×C139D411yescharacteristic
188C22⋊C8×C139D411yescharacteristic
189C22⋊C8×C139D411yescharacteristic
190C24×C139—21no—
191C24×C139—21no—
192C24×C139—21no—
193C24×C139#4111yescharacteristic
194#41×C139—21no—
195#41×C139—21no—
196#41×C139—24no—
197#41×C139—24no—
198#41×C139—22no—
199#41×C139—22no—
200#41×C139—21no—
201#41×C139—21no—
202#41×C139—21no—
203#41×C139—21no—
204#41×C139—42no—
205#41×C139—42no—
206#41×C139—41no—
207#41×C139—41no—
208#41×C139—42no—
209#41×C139—42no—
210#41×C139—42no—
211#41×C139—42no—
212#41×C139—42no—
213#41×C139—42no—
214#41×C139—42no—
215#41×C139—42no—
216#41×C139C2×D412yes—
217#41×C139C2×D412yes—
218C2×Q8×C139—21no—
219C2×Q8×C139—21no—
220C2×Q8×C139—22no—
221C2×Q8×C139—21no—
222C2×Q8×C139—21no—
223C2×Q8×C139—21no—
224C2×Q8×C139—21no—
225C2×Q8×C139—41no—
226C2×Q8×C139C2×D412yes—
227C2×Q8×C139C2×D411yescharacteristic
228C2×Q8×C139C2×D411yescharacteristic
229C2×D4×C139—21no—
230C2×D4×C139—22no—
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—21no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—21no—
243C2×D4×C139—21no—
244C2×D4×C139—21no—
245C2×D4×C139—21no—
246C2×D4×C139—41no—
247C2×D4×C139—42no—
248C2×D4×C139—42no—
249C2×D4×C139—42no—
250C2×D4×C139—42no—
251C2×D4×C139—41no—
252C2×D4×C139—41no—
253C2×D4×C139—41no—
254C2×D4×C139—41no—
255C2×D4×C139—82no—
256C2×D4×C139C2×D412yes—
257C2×D4×C139C2×D411yescharacteristic
258C2×D4×C139C2×D411yescharacteristic
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
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—42no—
271C22×C4×C139—42no—
272C22×C4×C139—42no—
273C22×C4×C139—42no—
274C22×C4×C139—41no—
275C22×C4×C139—41no—
276C22×C4×C139C2×D411yescharacteristic
277C22×C4×C139C2×D411yescharacteristic
278C22×C4×C139C2×D411yescharacteristic
279C22×C4×C139C2×D411yescharacteristic
280C22×C4×C139#4111yescharacteristic
281C22×C4×C139C2411yescharacteristic
282Q16×C139—24no—
283Q16×C139—24no—
284SD16×C139—24no—
285SD16×C139—24no—
286SD16×C139—24no—
287SD16×C139—24no—
288SD16×C139—42no—
289SD16×C139—42no—
290SD16×C139—42no—
291SD16×C139—42no—
292D8×C139—24no—
293D8×C139—24no—
294D8×C139—42no—
295D8×C139—42no—
296D8×C139—42no—
297D8×C139—42no—
298M16×C139—24no—
299M16×C139—21no—
300M16×C139—21no—
301M16×C139—21no—
302M16×C139—21no—
303M16×C139—21no—
304M16×C139—21no—
305M16×C139—21no—
306M16×C139—21no—
307M16×C139—21no—
308M16×C139—21no—
309M16×C139—42no—
310M16×C139—42no—
311M16×C139C2×D412yes—
312M16×C139C2×D412yes—
313C2×C8×C139—24no—
314C2×C8×C139—21no—
315C2×C8×C139—21no—
316C2×C8×C139—21no—
317C2×C8×C139—21no—
318C2×C8×C139—21no—
319C2×C8×C139—21no—
320C2×C8×C139—21no—
321C2×C8×C139—21no—
322C2×C8×C139—21no—
323C2×C8×C139—21no—
324C2×C8×C139—42no—
325C2×C8×C139—42no—
326C2×C8×C139C2×D411yescharacteristic
327C2×C8×C139C2×D411yescharacteristic
328C2×C8×C139C2×D411yescharacteristic
329C2×C8×C139C2×D411yescharacteristic
330C4⋊C4×C139—21no—
331C4⋊C4×C139—21no—
332C22⋊C4×C139—41no—
333C22⋊C4×C139—41no—
334C23×C139—21no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—22no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—42no—
342C23×C139—42no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—41no—
348C23×C139—81no—
349C23×C139—81no—
350C23×C139—81no—
351C23×C139—81no—
352C23×C139—81no—
353C23×C139#12111yescharacteristic
354C23×C139#12111yescharacteristic
355C23×C139C2×#4111yescharacteristic
356Q8×C139—21no—
357Q8×C139—21no—
358Q8×C139—22no—
359Q8×C139—21no—
360Q8×C139—22no—
361Q8×C139—42no—
362Q8×C139—41no—
363Q8×C139—41no—
364Q8×C139#12012yes—
365D4×C139—22no—
366D4×C139—22no—
367D4×C139—21no—
368D4×C139—22no—
369D4×C139—21no—
370D4×C139—21no—
371D4×C139—22no—
372D4×C139—42no—
373D4×C139—42no—
374D4×C139—42no—
375D4×C139—44no—
376D4×C139—44no—
377D4×C139—41no—
378D4×C139—41no—
379D4×C139—41no—
380D4×C139—41no—
381D4×C139—41no—
382D4×C139—41no—
383D4×C139—41no—
384D4×C139—41no—
385D4×C139—82no—
386D4×C139—82no—
387D4×C139#12012yes—
388C2×C4×C139—21no—
389C2×C4×C139—21no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—21no—
395C2×C4×C139—22no—
396C2×C4×C139—22no—
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—21no—
402C2×C4×C139—22no—
403C2×C4×C139—42no—
404C2×C4×C139—42no—
405C2×C4×C139—42no—
406C2×C4×C139—44no—
407C2×C4×C139—44no—
408C2×C4×C139—41no—
409C2×C4×C139—41no—
410C2×C4×C139—41no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
413C2×C4×C139—81no—
414C2×C4×C139#12111yescharacteristic
415C2×C4×C139#12111yescharacteristic
416C2×C4×C139C22×D411yescharacteristic
417C2×C4×C139C22×D411yescharacteristic
418C2×C4×C139C22×D411yescharacteristic
419C2×C4×C139C22×D411yescharacteristic
420C2×C4×C139H(5,𝔽2)11yescharacteristic
421C2×C4×C139H(5,𝔽2)11yescharacteristic
422C8×C139—22no—
423C8×C139—22no—
424C8×C139—21no—
425C8×C139—21no—
426C8×C139—21no—
427C8×C139—21no—
428C8×C139—41no—
429C8×C139—41no—
430C8×C139—41no—
431C8×C139—41no—
432C22×C139—21no—
433C22×C139—21no—
434C22×C139—21no—
435C22×C139—21no—
436C22×C139—22no—
437C22×C139—21no—
438C22×C139—21no—
439C22×C139—21no—
440C22×C139—21no—
441C22×C139—41no—
442C22×C139—41no—
443C22×C139—41no—
444C22×C139—42no—
445C22×C139—41no—
446C22×C139—41no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139—82no—
450C22×C139—82no—
451C22×C139—84no—
452C22×C139—81no—
453C22×C139—81no—
454C22×C139—81no—
455C22×C139—81no—
456C22×C139—81no—
457C22×C139—161no—
458C22×C139—161no—
459C22×C139C2×#12111yescharacteristic
460C22×C139#54611yescharacteristic
461C22×C139#54611yescharacteristic
462C4×C139—21no—
463C4×C139—21no—
464C4×C139—22no—
465C4×C139—41no—
466C4×C139—42no—
467C4×C139—81no—
468C4×C139C2×#12011yescharacteristic
469C4×C139#53411yescharacteristic
470C4×C139D4211yescharacteristic
471C4×C139D4211yescharacteristic
472C2×C139—21no—
473C2×C139—21no—
474C2×C139—41no—
475C2×C139—41no—
476C2×C139—42no—
477C2×C139—81no—
478C2×C139—82no—
479C2×C139—161no—
480C2×C139#241011yescharacteristic
481C2×C139#306711yescharacteristic
482C2×C139#306811yescharacteristic
483#24402C13911yesmaximal, characteristic, direct product factor, Sylow
484C139#2440211yescharacteristic, direct product factor, Sylow
485C2×#575C2×C13911yescharacteristic, complemented
486C2×#472C2×C13911yescharacteristic, complemented
487C2×#471C2×C13911yescharacteristic, complemented
488#3006C2×C13911yescharacteristic, complemented
489C2×#449C2×C13911yescharacteristic, complemented
490#2880C2×C13911yescharacteristic, complemented
491#2052C2×C13911yescharacteristic, complemented
492#2051C2×C13911yescharacteristic, complemented
493#2019C2×C13911yescharacteristic, complemented
494#2018C2×C13911yescharacteristic, complemented
495#1908C2×C13911yescharacteristic, complemented
496#1907C2×C13911yescharacteristic, complemented
497#1900C2×C13911yescharacteristic, complemented
498#1855C2×C13911yescharacteristic, complemented
499#1785C2×C13911yescharacteristic, complemented
500C22×#41C22×C13911yescharacteristic
501C22×#41C22×C13911yescharacteristic
502#575—24no—
503#575—24no—
504C2×#137—21no—
505C2×#137C22×C13911yescharacteristic
506C2×#137C22×C13911yescharacteristic
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
509C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
510C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
511C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
512C2×#135—21no—
513C2×#135—21no—
514C22×SD16C22×C13911yescharacteristic, complemented
515C22×D8C22×C13911yescharacteristic, complemented
516C2×#131C22×C13911yescharacteristic
517C2×#131C22×C13911yescharacteristic
518C22×M16C22×C13911yescharacteristic
519C2×#121C22×C13911yescharacteristic
520#472—24no—
521#471—24no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#449—21no—
528#448—21no—
529#447—21no—
530C2×#108C22×C13911yescharacteristic, complemented
531C2×#108C22×C13911yescharacteristic, complemented
532#417C22×C13911yescharacteristic
533#417C22×C13911yescharacteristic
534C2×#103C22×C13911yescharacteristic, complemented
535C2×#102C22×C13911yescharacteristic, complemented
536C2×#101C22×C13911yescharacteristic, complemented
537C2×#101C22×C13911yescharacteristic, complemented
538C2×#100C22×C13911yescharacteristic, complemented
539C2×#100C22×C13911yescharacteristic, complemented
540C2×#100C22×C13911yescharacteristic, complemented
541C2×#100C22×C13911yescharacteristic, complemented
542#408—21no—
543#408—21no—
544#408C22×C13911yescharacteristic
545#408C22×C13911yescharacteristic
546#407—21no—
547#407C22×C13911yescharacteristic
548#407C22×C13911yescharacteristic
549C2×C22⋊C8—21no—
550C2×C22⋊C8C22×C13911yescharacteristic
551#343C22×C13911yescharacteristic, complemented
552#343C22×C13911yescharacteristic, complemented
553#341C22×C13911yescharacteristic, complemented
554#341C22×C13911yescharacteristic, complemented
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C13911yescharacteristic
570C2×#41D4×C13911yescharacteristic
571C2×#41C23×C13911yescharacteristic
572C2×#41C23×C13911yescharacteristic
573C22×Q8D4×C13911yescharacteristic
574C22×Q8C23×C13911yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C13911yescharacteristic
579C22×D4C23×C13911yescharacteristic
580C22×D4C23×C13911yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C13911yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C13914yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C13914yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C13911yescharacteristic
630C2×M16C23×C13911yescharacteristic
631C2×M16C23×C13911yescharacteristic
632C2×M16C23×C13911yescharacteristic
633C2×M16C23×C13911yescharacteristic
634C2×M16C23×C13911yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C13911yescharacteristic
639C22×C8C23×C13911yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C13911yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C13911yescharacteristic
671C22⋊C8D4×C13911yescharacteristic
672C22⋊C8D4×C13911yescharacteristic
673C22⋊C8D4×C13911yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C13911yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C13912yes—
701#41C2×D4×C13912yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C13912yes—
711C2×Q8C2×D4×C13911yescharacteristic
712C2×Q8C2×D4×C13911yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C13912yes—
741C2×D4C2×D4×C13911yescharacteristic
742C2×D4C2×D4×C13911yescharacteristic
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—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C13911yescharacteristic
761C22×C4C2×D4×C13911yescharacteristic
762C22×C4C2×D4×C13911yescharacteristic
763C22×C4C2×D4×C13911yescharacteristic
764C22×C4#41×C13911yescharacteristic
765C22×C4C24×C13911yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C13912yes—
796M16C2×D4×C13912yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C13911yescharacteristic
811C2×C8C2×D4×C13911yescharacteristic
812C2×C8C2×D4×C13911yescharacteristic
813C2×C8C2×D4×C13911yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C13911yescharacteristic
838C23#121×C13911yescharacteristic
839C23C2×#41×C13911yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C13912yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C13912yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C13911yescharacteristic
899C2×C4#121×C13911yescharacteristic
900C2×C4C22×D4×C13911yescharacteristic
901C2×C4C22×D4×C13911yescharacteristic
902C2×C4C22×D4×C13911yescharacteristic
903C2×C4C22×D4×C13911yescharacteristic
904C2×C4H(5,𝔽2)×C13911yescharacteristic
905C2×C4H(5,𝔽2)×C13911yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C13911yescharacteristic
944C22#546×C13911yescharacteristic
945C22#546×C13911yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C13911yescharacteristic
953C4#534×C13911yescharacteristic
954C4D42×C13911yescharacteristic
955C4D42×C13911yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2#2410×C13911yescharacteristic
965C2#3067×C13911yescharacteristic
966C2#3068×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C139C2semidirect
2. C2×#472×C139C2semidirect
3. C2×#471×C139C2semidirect
4. #3006×C139C2semidirect
5. C2×#449×C139C2semidirect
6. #2880×C139C2semidirect
7. #2052×C139C2semidirect
8. #2051×C139C2semidirect
9. #2019×C139C2semidirect
10. #2018×C139C2semidirect
11. #1908×C139C2semidirect
12. #1907×C139C2semidirect
13. #1900×C139C2semidirect
14. #1855×C139C2semidirect
15. #1785×C139C2semidirect
30. C22×SD16×C139C22semidirect
31. C22×D8×C139C22semidirect
46. C2×#108×C139C22semidirect
47. C2×#108×C139C22semidirect
50. C2×#103×C139C22semidirect
51. C2×#102×C139C22semidirect
52. C2×#101×C139C22semidirect
53. C2×#101×C139C22semidirect
54. C2×#100×C139C22semidirect
55. C2×#100×C139C22semidirect
56. C2×#100×C139C22semidirect
57. C2×#100×C139C22semidirect
67. #343×C139C22semidirect
68. #343×C139C22semidirect
69. #341×C139C22semidirect
70. #341×C139C22semidirect
104. #137×C139D4semidirect
113. AGL(1,ℤ/8)×C139D4semidirect
483. #24402C139direct (N × H)
484. C139#24402direct (N × H)
485. C2×#575C2×C139semidirect
486. C2×#472C2×C139semidirect
487. C2×#471C2×C139semidirect
488. #3006C2×C139semidirect
489. C2×#449C2×C139semidirect
490. #2880C2×C139semidirect
491. #2052C2×C139semidirect
492. #2051C2×C139semidirect
493. #2019C2×C139semidirect
494. #2018C2×C139semidirect
495. #1908C2×C139semidirect
496. #1907C2×C139semidirect
497. #1900C2×C139semidirect
498. #1855C2×C139semidirect
499. #1785C2×C139semidirect
514. C22×SD16C22×C139semidirect
515. C22×D8C22×C139semidirect
530. C2×#108C22×C139semidirect
531. C2×#108C22×C139semidirect
534. C2×#103C22×C139semidirect
535. C2×#102C22×C139semidirect
536. C2×#101C22×C139semidirect
537. C2×#101C22×C139semidirect
538. C2×#100C22×C139semidirect
539. C2×#100C22×C139semidirect
540. C2×#100C22×C139semidirect
541. C2×#100C22×C139semidirect
551. #343C22×C139semidirect
552. #343C22×C139semidirect
553. #341C22×C139semidirect
554. #341C22×C139semidirect
588. #137D4×C139semidirect
597. AGL(1,ℤ/8)D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1392
C2×#472×C1392
C2×#471×C1392
#3006×C1392
C2×#449×C1392
#2880×C1392
#2052×C1392
#2051×C1392
#2019×C1392
#2018×C1392
#1908×C1392
#1907×C1392
#1900×C1392
#1855×C1392
#1785×C1392
#24402139