Finite Group Databasebeta

← C139×#24467 #48019063

Subgroups — C139×#24467 #48019063

Order 35584.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C139C211yesmaximal, characteristic
2#3056×C139C211yesmaximal, characteristic, complemented
3C2×#455×C139C211yesmaximal, characteristic, complemented
4#3007×C139C211yesmaximal, characteristic, complemented
5C22×#104×C139C211yesmaximal, characteristic, complemented
6#2850×C139C211yesmaximal, characteristic, complemented
7#2040×C139C211yesmaximal, characteristic, complemented
8#2037×C139C211yesmaximal, characteristic, complemented
9#2007×C139C211yesmaximal, characteristic, complemented
10#2004×C139C211yesmaximal, characteristic, complemented
11#1900×C139C211yesmaximal, characteristic, complemented
12#1896×C139C211yesmaximal, characteristic, complemented
13#1882×C139C211yesmaximal, characteristic, complemented
14#1860×C139C211yesmaximal, characteristic, complemented
15#1792×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C2×#137×C139C2211yescharacteristic
19C2×#137×C139C2211yescharacteristic, complemented
20C2×#137×C139C2211yescharacteristic, complemented
21C22×M16×C139C2211yescharacteristic, complemented
22#550×C139—21no—
23#548×C139—21no—
24#546×C139—21no—
25#546×C139—22no—
26D42×C139—22no—
27D42×C139—21no—
28#537×C139—21no—
29#537×C139C2211yescharacteristic
30#535×C139—21no—
31#535×C139C2211yescharacteristic
32C2×#124×C139C2211yescharacteristic, complemented
33#525×C139—21no—
34#525×C139C2211yescharacteristic
35C2×C22⋊Q8×C139C2211yescharacteristic, complemented
36C2×#121×C139—21no—
37C2×#121×C139C2211yescharacteristic
38#520×C139C2211yescharacteristic
39C22×C42×C139C2211yescharacteristic, complemented
40#470×C139—21no—
41#468×C139—21no—
42#467×C139—21no—
43#465×C139—21no—
44#455×C139—24no—
45#452×C139—21no—
46#452×C139—21no—
47#451×C139—21no—
48#450×C139—21no—
49#428×C139C2211yescharacteristic, complemented
50C2×#104×C139—24no—
51C2×#104×C139C2211yescharacteristic
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic, complemented
54C2×#104×C139C2211yescharacteristic, complemented
55C2×#104×C139C2211yescharacteristic, complemented
56C2×#104×C139C2211yescharacteristic, complemented
57#419×C139C2211yescharacteristic, complemented
58#417×C139C2211yescharacteristic
59#417×C139C2211yescharacteristic, complemented
60#417×C139C2211yescharacteristic, complemented
61C2×#100×C139C2211yescharacteristic, complemented
62C2×#100×C139C2211yescharacteristic, complemented
63#407×C139C2211yescharacteristic, complemented
64#391×C139C2211yescharacteristic, complemented
65#390×C139C2211yescharacteristic, complemented
66#388×C139—22no—
67#386×C139—22no—
68#382×C139C2211yescharacteristic, complemented
69#343×C139C2211yescharacteristic, complemented
70#343×C139C2211yescharacteristic, complemented
71#339×C139C2211yescharacteristic, complemented
72#339×C139C2211yescharacteristic, complemented
73H(5,𝔽2)×C139—22no—
74H(5,𝔽2)×C139—22no—
75H(5,𝔽2)×C139—41no—
76H(5,𝔽2)×C139—41no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—22no—
82C2×#41×C139—22no—
83C2×#41×C139—41no—
84C2×#41×C139—41no—
85C2×#41×C139D411yescharacteristic
86C2×#41×C139D411yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C2×#41×C139C2311yescharacteristic
90C22×Q8×C139D411yescharacteristic
91C22×Q8×C139C2311yescharacteristic
92C22×D4×C139—21no—
93C22×D4×C139—22no—
94C22×D4×C139—22no—
95C22×D4×C139—21no—
96C22×D4×C139—21no—
97C22×D4×C139D411yescharacteristic
98C22×D4×C139D412yes—
99C22×D4×C139C2311yescharacteristic
100C23×C4×C139—21no—
101C23×C4×C139—21no—
102C23×C4×C139C2311yescharacteristic
103#137×C139—22no—
104#137×C139—22no—
105#137×C139—22no—
106#137×C139—41no—
107#137×C139—41no—
108#137×C139—41no—
109C2×Q16×C139—21no—
110C2×Q16×C139—21no—
111C2×Q16×C139—21no—
112C2×SD16×C139—21no—
113C2×SD16×C139—21no—
114C2×SD16×C139—21no—
115C2×M16×C139—21no—
116C2×M16×C139—22no—
117C2×M16×C139—41no—
118C2×M16×C139C2311yescharacteristic
119C2×M16×C139C2311yescharacteristic
120C2×M16×C139C2311yescharacteristic
121C2×M16×C139C2311yescharacteristic
122C22×C8×C139—21no—
123#127×C139—22no—
124#127×C139—21no—
125#124×C139—22no—
126#124×C139—21no—
127#124×C139—22no—
128#124×C139—41no—
129#123×C139—22no—
130#123×C139—21no—
131C22⋊Q8×C139—22no—
132C22⋊Q8×C139—21no—
133C22⋊Q8×C139—21no—
134C22⋊Q8×C139—21no—
135C22⋊Q8×C139—21no—
136C22⋊Q8×C139—21no—
137C22⋊Q8×C139—21no—
138C22⋊Q8×C139D411yescharacteristic
139C22⋊Q8×C139D411yescharacteristic
140#121×C139—22no—
141#121×C139—22no—
142#121×C139—22no—
143#121×C139—22no—
144#121×C139—22no—
145#121×C139—21no—
146#121×C139—21no—
147#121×C139—21no—
148#121×C139—21no—
149#121×C139—21no—
150#121×C139—21no—
151#121×C139—22no—
152#121×C139—21no—
153#121×C139—21no—
154#121×C139D411yescharacteristic
155#121×C139D411yescharacteristic
156#120×C139—22no—
157#120×C139—22no—
158#120×C139—22no—
159#120×C139—21no—
160#120×C139—22no—
161C4×Q8×C139—21no—
162C4×D4×C139—22no—
163C4×D4×C139—22no—
164C4×D4×C139—21no—
165C4×D4×C139—22no—
166C4×D4×C139—21no—
167C4×D4×C139—21no—
168#117×C139—21no—
169#117×C139C2311yescharacteristic
170C2×C4⋊C4×C139—21no—
171C2×C4⋊C4×C139—21no—
172C2×C4⋊C4×C139C2311yescharacteristic
173C2×C4⋊C4×C139C2311yescharacteristic
174C2×C22⋊C4×C139—22no—
175C2×C22⋊C4×C139—21no—
176C2×C22⋊C4×C139—22no—
177C2×C22⋊C4×C139—22no—
178C2×C22⋊C4×C139D412yes—
179C2×C42×C139—22no—
180C2×C42×C139—21no—
181C2×C42×C139—41no—
182C2×C42×C139C2311yescharacteristic
183C2×C42×C139C2311yescharacteristic
184#107×C139—21no—
185#106×C139—21no—
186#104×C139—22no—
187#104×C139—22no—
188#104×C139—22no—
189#104×C139—22no—
190#104×C139—41no—
191#104×C139D414yescomplemented
192#103×C139—21no—
193#103×C139—21no—
194#103×C139—21no—
195#103×C139—21no—
196#103×C139—21no—
197#102×C139—21no—
198#102×C139—21no—
199#102×C139—21no—
200#100×C139—22no—
201#100×C139—41no—
202C22⋊C8×C139—21no—
203C22⋊C8×C139—21no—
204#95×C139—22no—
205#95×C139—22no—
206C24×C139—22no—
207C24×C139—21no—
208C24×C139C2×D411yescharacteristic
209C24×C139C2×D412yes—
210#41×C139—21no—
211#41×C139—21no—
212#41×C139—22no—
213#41×C139—22no—
214#41×C139—21no—
215#41×C139—21no—
216#41×C139—21no—
217#41×C139—21no—
218#41×C139—21no—
219#41×C139—21no—
220#41×C139—21no—
221#41×C139—21no—
222#41×C139—42no—
223#41×C139—42no—
224#41×C139—41no—
225#41×C139—41no—
226#41×C139—42no—
227#41×C139—42no—
228#41×C139—42no—
229#41×C139—42no—
230#41×C139—42no—
231#41×C139—42no—
232#41×C139C2×D412yes—
233#41×C139#4112yes—
234C2×Q8×C139—21no—
235C2×Q8×C139—22no—
236C2×Q8×C139—21no—
237C2×Q8×C139—21no—
238C2×Q8×C139—21no—
239C2×Q8×C139—21no—
240C2×Q8×C139—21no—
241C2×Q8×C139—21no—
242C2×Q8×C139—41no—
243C2×Q8×C139C2×D411yescharacteristic
244C2×Q8×C139C2×D411yescharacteristic
245C2×Q8×C139C2×D411yescharacteristic
246C2×D4×C139—21no—
247C2×D4×C139—22no—
248C2×D4×C139—22no—
249C2×D4×C139—22no—
250C2×D4×C139—22no—
251C2×D4×C139—21no—
252C2×D4×C139—21no—
253C2×D4×C139—21no—
254C2×D4×C139—21no—
255C2×D4×C139—21no—
256C2×D4×C139—22no—
257C2×D4×C139—22no—
258C2×D4×C139—22no—
259C2×D4×C139—21no—
260C2×D4×C139—22no—
261C2×D4×C139—21no—
262C2×D4×C139—21no—
263C2×D4×C139—21no—
264C2×D4×C139—21no—
265C2×D4×C139—21no—
266C2×D4×C139—21no—
267C2×D4×C139—21no—
268C2×D4×C139—41no—
269C2×D4×C139—42no—
270C2×D4×C139—42no—
271C2×D4×C139—42no—
272C2×D4×C139—42no—
273C2×D4×C139—44no—
274C2×D4×C139—44no—
275C2×D4×C139—42no—
276C2×D4×C139—42no—
277C2×D4×C139—44no—
278C2×D4×C139—84no—
279C2×D4×C139C2×D411yescharacteristic
280C2×D4×C139C2×D411yescharacteristic
281C2×D4×C139C2×D411yescharacteristic
282C22×C4×C139—21no—
283C22×C4×C139—21no—
284C22×C4×C139—21no—
285C22×C4×C139—21no—
286C22×C4×C139—21no—
287C22×C4×C139—22no—
288C22×C4×C139—21no—
289C22×C4×C139—21no—
290C22×C4×C139—21no—
291C22×C4×C139—22no—
292C22×C4×C139—21no—
293C22×C4×C139—21no—
294C22×C4×C139—21no—
295C22×C4×C139—21no—
296C22×C4×C139—21no—
297C22×C4×C139—21no—
298C22×C4×C139—42no—
299C22×C4×C139—42no—
300C22×C4×C139—42no—
301C22×C4×C139—42no—
302C22×C4×C139—42no—
303C22×C4×C139C2×D411yescharacteristic
304C22×C4×C139C2×D411yescharacteristic
305C22×C4×C139C2×D411yescharacteristic
306C22×C4×C139C2×D411yescharacteristic
307C22×C4×C139C2×D411yescharacteristic
308C22×C4×C139C2×D412yes—
309C22×C4×C139C2411yescharacteristic
310Q16×C139—42no—
311Q16×C139—42no—
312Q16×C139—42no—
313SD16×C139—42no—
314SD16×C139—42no—
315SD16×C139—42no—
316M16×C139—21no—
317M16×C139—21no—
318M16×C139—21no—
319M16×C139—21no—
320M16×C139—21no—
321M16×C139—21no—
322M16×C139—21no—
323M16×C139—42no—
324M16×C139C2×D412yescomplemented
325C2×C8×C139—21no—
326C2×C8×C139—21no—
327C2×C8×C139—21no—
328C2×C8×C139—21no—
329C2×C8×C139—42no—
330C4⋊C4×C139—22no—
331C4⋊C4×C139—22no—
332C4⋊C4×C139—21no—
333C4⋊C4×C139—21no—
334C4⋊C4×C139—21no—
335C4⋊C4×C139—21no—
336C4⋊C4×C139—21no—
337C4⋊C4×C139—21no—
338C4⋊C4×C139—41no—
339C4⋊C4×C139—41no—
340C4⋊C4×C139C2×D411yescharacteristic
341C4⋊C4×C139C2×D411yescharacteristic
342C22⋊C4×C139—22no—
343C22⋊C4×C139—22no—
344C22⋊C4×C139—22no—
345C22⋊C4×C139—22no—
346C22⋊C4×C139—22no—
347C22⋊C4×C139—21no—
348C22⋊C4×C139—21no—
349C22⋊C4×C139—21no—
350C22⋊C4×C139—21no—
351C22⋊C4×C139—22no—
352C22⋊C4×C139—22no—
353C22⋊C4×C139—21no—
354C22⋊C4×C139—44no—
355C22⋊C4×C139—44no—
356C22⋊C4×C139—41no—
357C22⋊C4×C139—41no—
358C42×C139—22no—
359C42×C139—21no—
360C42×C139—21no—
361C42×C139—21no—
362C42×C139—21no—
363C42×C139—42no—
364C42×C139C2×D412yescomplemented
365C23×C139—21no—
366C23×C139—21no—
367C23×C139—21no—
368C23×C139—22no—
369C23×C139—22no—
370C23×C139—21no—
371C23×C139—21no—
372C23×C139—22no—
373C23×C139—22no—
374C23×C139—41no—
375C23×C139—42no—
376C23×C139—44no—
377C23×C139—42no—
378C23×C139—42no—
379C23×C139—42no—
380C23×C139—81no—
381C23×C139—82no—
382C23×C139—82no—
383C23×C139#12011yescharacteristic
384C23×C139#12011yescharacteristic
385C23×C139C22×D411yescharacteristic
386Q8×C139—21no—
387Q8×C139—21no—
388Q8×C139—21no—
389Q8×C139—21no—
390Q8×C139—21no—
391Q8×C139—42no—
392Q8×C139—41no—
393Q8×C139—41no—
394Q8×C139—41no—
395Q8×C139—41no—
396Q8×C139#12112yes—
397D4×C139—22no—
398D4×C139—22no—
399D4×C139—21no—
400D4×C139—21no—
401D4×C139—21no—
402D4×C139—21no—
403D4×C139—21no—
404D4×C139—42no—
405D4×C139—42no—
406D4×C139—44no—
407D4×C139—42no—
408D4×C139—44no—
409D4×C139—41no—
410D4×C139—41no—
411D4×C139—41no—
412D4×C139—41no—
413D4×C139—44no—
414D4×C139—42no—
415D4×C139—41no—
416D4×C139—41no—
417D4×C139—41no—
418D4×C139—41no—
419D4×C139—81no—
420D4×C139—82no—
421D4×C139—82no—
422D4×C139—82no—
423D4×C139—82no—
424D4×C139#12112yes—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—21no—
428C2×C4×C139—21no—
429C2×C4×C139—21no—
430C2×C4×C139—21no—
431C2×C4×C139—21no—
432C2×C4×C139—21no—
433C2×C4×C139—21no—
434C2×C4×C139—22no—
435C2×C4×C139—21no—
436C2×C4×C139—21no—
437C2×C4×C139—22no—
438C2×C4×C139—22no—
439C2×C4×C139—21no—
440C2×C4×C139—22no—
441C2×C4×C139—21no—
442C2×C4×C139—21no—
443C2×C4×C139—21no—
444C2×C4×C139—22no—
445C2×C4×C139—42no—
446C2×C4×C139—42no—
447C2×C4×C139—42no—
448C2×C4×C139—44no—
449C2×C4×C139—41no—
450C2×C4×C139—41no—
451C2×C4×C139—41no—
452C2×C4×C139—48no—
453C2×C4×C139—41no—
454C2×C4×C139—41no—
455C2×C4×C139—41no—
456C2×C4×C139—41no—
457C2×C4×C139—41no—
458C2×C4×C139—42no—
459C2×C4×C139—42no—
460C2×C4×C139—41no—
461C2×C4×C139—41no—
462C2×C4×C139—41no—
463C2×C4×C139—41no—
464C2×C4×C139—82no—
465C2×C4×C139#12011yescharacteristic
466C2×C4×C139#12011yescharacteristic
467C2×C4×C139C22×D411yescharacteristic
468C2×C4×C139C22×D411yescharacteristic
469C2×C4×C139C22×D411yescharacteristic
470C2×C4×C139C2×#4111yescharacteristic
471C2×C4×C139H(5,𝔽2)11yescharacteristic
472C2×C4×C139H(5,𝔽2)11yescharacteristic
473C8×C139—22no—
474C8×C139—41no—
475C8×C139—41no—
476C8×C139—41no—
477C22×C139—21no—
478C22×C139—21no—
479C22×C139—21no—
480C22×C139—21no—
481C22×C139—21no—
482C22×C139—22no—
483C22×C139—21no—
484C22×C139—21no—
485C22×C139—42no—
486C22×C139—42no—
487C22×C139—41no—
488C22×C139—41no—
489C22×C139—41no—
490C22×C139—41no—
491C22×C139—42no—
492C22×C139—42no—
493C22×C139—41no—
494C22×C139—41no—
495C22×C139—41no—
496C22×C139—42no—
497C22×C139—41no—
498C22×C139—84no—
499C22×C139—82no—
500C22×C139—82no—
501C22×C139—164no—
502C22×C139#45512yescomplemented
503C22×C139C2×#12011yescharacteristic
504C22×C139D4211yescharacteristic
505C22×C139#54611yescharacteristic
506C4×C139—21no—
507C4×C139—21no—
508C4×C139—22no—
509C4×C139—42no—
510C4×C139—42no—
511C4×C139—41no—
512C4×C139—41no—
513C4×C139—42no—
514C4×C139—41no—
515C4×C139—41no—
516C4×C139—81no—
517C4×C139—81no—
518C4×C139C2×#12111yescharacteristic
519C4×C139#53411yescharacteristic
520C4×C139D4211yescharacteristic
521C4×C139#54611yescharacteristic
522C2×C139—21no—
523C2×C139—21no—
524C2×C139—22no—
525C2×C139—41no—
526C2×C139—42no—
527C2×C139—81no—
528C2×C139—82no—
529C2×C139—81no—
530C2×C139#241011yescharacteristic
531C2×C139C2×#45511yescharacteristic
532C2×C139#301811yescharacteristic
533#24467C13911yesmaximal, characteristic, direct product factor, Sylow
534C139#2446711yescharacteristic, direct product factor, Sylow
535#3488C2×C13911yescharacteristic
536#3056C2×C13911yescharacteristic, complemented
537C2×#455C2×C13911yescharacteristic, complemented
538#3007C2×C13911yescharacteristic, complemented
539C22×#104C2×C13911yescharacteristic, complemented
540#2850C2×C13911yescharacteristic, complemented
541#2040C2×C13911yescharacteristic, complemented
542#2037C2×C13911yescharacteristic, complemented
543#2007C2×C13911yescharacteristic, complemented
544#2004C2×C13911yescharacteristic, complemented
545#1900C2×C13911yescharacteristic, complemented
546#1896C2×C13911yescharacteristic, complemented
547#1882C2×C13911yescharacteristic, complemented
548#1860C2×C13911yescharacteristic, complemented
549#1792C2×C13911yescharacteristic, complemented
550C2×H(5,𝔽2)C22×C13911yescharacteristic
551C22×#41C22×C13911yescharacteristic
552C2×#137C22×C13911yescharacteristic
553C2×#137C22×C13911yescharacteristic, complemented
554C2×#137C22×C13911yescharacteristic, complemented
555C22×M16C22×C13911yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C13911yescharacteristic
564#535—21no—
565#535C22×C13911yescharacteristic
566C2×#124C22×C13911yescharacteristic, complemented
567#525—21no—
568#525C22×C13911yescharacteristic
569C2×C22⋊Q8C22×C13911yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C13911yescharacteristic
572#520C22×C13911yescharacteristic
573C22×C42C22×C13911yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C13911yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C13911yescharacteristic
586C2×#104C22×C13911yescharacteristic
587C2×#104C22×C13911yescharacteristic, complemented
588C2×#104C22×C13911yescharacteristic, complemented
589C2×#104C22×C13911yescharacteristic, complemented
590C2×#104C22×C13911yescharacteristic, complemented
591#419C22×C13911yescharacteristic, complemented
592#417C22×C13911yescharacteristic
593#417C22×C13911yescharacteristic, complemented
594#417C22×C13911yescharacteristic, complemented
595C2×#100C22×C13911yescharacteristic, complemented
596C2×#100C22×C13911yescharacteristic, complemented
597#407C22×C13911yescharacteristic, complemented
598#391C22×C13911yescharacteristic, complemented
599#390C22×C13911yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C13911yescharacteristic, complemented
603#343C22×C13911yescharacteristic, complemented
604#343C22×C13911yescharacteristic, complemented
605#339C22×C13911yescharacteristic, complemented
606#339C22×C13911yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C13911yescharacteristic
620C2×#41D4×C13911yescharacteristic
621C2×#41C23×C13911yescharacteristic
622C2×#41C23×C13911yescharacteristic
623C2×#41C23×C13911yescharacteristic
624C22×Q8D4×C13911yescharacteristic
625C22×Q8C23×C13911yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C13911yescharacteristic
632C22×D4D4×C13912yes—
633C22×D4C23×C13911yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C13911yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C13911yescharacteristic
653C2×M16C23×C13911yescharacteristic
654C2×M16C23×C13911yescharacteristic
655C2×M16C23×C13911yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C13911yescharacteristic
673C22⋊Q8D4×C13911yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C13911yescharacteristic
689#121D4×C13911yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C13911yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C13911yescharacteristic
707C2×C4⋊C4C23×C13911yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C13912yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C13911yescharacteristic
717C2×C42C23×C13911yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C13914yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C13911yescharacteristic
743C24C2×D4×C13912yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C13912yes—
767#41#41×C13912yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C13911yescharacteristic
778C2×Q8C2×D4×C13911yescharacteristic
779C2×Q8C2×D4×C13911yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C13911yescharacteristic
814C2×D4C2×D4×C13911yescharacteristic
815C2×D4C2×D4×C13911yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C13911yescharacteristic
838C22×C4C2×D4×C13911yescharacteristic
839C22×C4C2×D4×C13911yescharacteristic
840C22×C4C2×D4×C13911yescharacteristic
841C22×C4C2×D4×C13911yescharacteristic
842C22×C4C2×D4×C13912yes—
843C22×C4C24×C13911yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C13912yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C13911yescharacteristic
875C4⋊C4C2×D4×C13911yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C13912yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C13911yescharacteristic
918C23#120×C13911yescharacteristic
919C23C22×D4×C13911yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C13912yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C13912yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C13911yescharacteristic
1000C2×C4#120×C13911yescharacteristic
1001C2×C4C22×D4×C13911yescharacteristic
1002C2×C4C22×D4×C13911yescharacteristic
1003C2×C4C22×D4×C13911yescharacteristic
1004C2×C4C2×#41×C13911yescharacteristic
1005C2×C4H(5,𝔽2)×C13911yescharacteristic
1006C2×C4H(5,𝔽2)×C13911yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C13912yescomplemented
1037C22C2×#120×C13911yescharacteristic
1038C22D42×C13911yescharacteristic
1039C22#546×C13911yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C13911yescharacteristic
1053C4#534×C13911yescharacteristic
1054C4D42×C13911yescharacteristic
1055C4#546×C13911yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2#2410×C13911yescharacteristic
1065C2C2×#455×C13911yescharacteristic
1066C2#3018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3488×C139C2
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
2. #3056×C139C2semidirect
3. C2×#455×C139C2semidirect
4. #3007×C139C2semidirect
5. C22×#104×C139C2semidirect
6. #2850×C139C2semidirect
7. #2040×C139C2semidirect
8. #2037×C139C2semidirect
9. #2007×C139C2semidirect
10. #2004×C139C2semidirect
11. #1900×C139C2semidirect
12. #1896×C139C2semidirect
13. #1882×C139C2semidirect
14. #1860×C139C2semidirect
15. #1792×C139C2semidirect
19. C2×#137×C139C22semidirect
20. C2×#137×C139C22semidirect
21. C22×M16×C139C22semidirect
32. C2×#124×C139C22semidirect
35. C2×C22⋊Q8×C139C22semidirect
39. C22×C42×C139C22semidirect
49. #428×C139C22semidirect
53. C2×#104×C139C22semidirect
54. C2×#104×C139C22semidirect
55. C2×#104×C139C22semidirect
56. C2×#104×C139C22semidirect
57. #419×C139C22semidirect
59. #417×C139C22semidirect
60. #417×C139C22semidirect
61. C2×#100×C139C22semidirect
62. C2×#100×C139C22semidirect
63. #407×C139C22semidirect
64. #391×C139C22semidirect
65. #390×C139C22semidirect
68. #382×C139C22semidirect
69. #343×C139C22semidirect
70. #343×C139C22semidirect
71. #339×C139C22semidirect
72. #339×C139C22semidirect
191. #104×C139D4semidirect
324. M16×C139C2×D4semidirect
364. C42×C139C2×D4semidirect
502. C22×C139#455semidirect
533. #24467C139direct (N × H)
534. C139#24467direct (N × H)
536. #3056C2×C139semidirect
537. C2×#455C2×C139semidirect
538. #3007C2×C139semidirect
539. C22×#104C2×C139semidirect
540. #2850C2×C139semidirect
541. #2040C2×C139semidirect
542. #2037C2×C139semidirect
543. #2007C2×C139semidirect
544. #2004C2×C139semidirect
545. #1900C2×C139semidirect
546. #1896C2×C139semidirect
547. #1882C2×C139semidirect
548. #1860C2×C139semidirect
549. #1792C2×C139semidirect
553. C2×#137C22×C139semidirect
554. C2×#137C22×C139semidirect
555. C22×M16C22×C139semidirect
566. C2×#124C22×C139semidirect
569. C2×C22⋊Q8C22×C139semidirect
573. C22×C42C22×C139semidirect
583. #428C22×C139semidirect
587. C2×#104C22×C139semidirect
588. C2×#104C22×C139semidirect
589. C2×#104C22×C139semidirect
590. C2×#104C22×C139semidirect
591. #419C22×C139semidirect
593. #417C22×C139semidirect
594. #417C22×C139semidirect
595. C2×#100C22×C139semidirect
596. C2×#100C22×C139semidirect
597. #407C22×C139semidirect
598. #391C22×C139semidirect
599. #390C22×C139semidirect
602. #382C22×C139semidirect
603. #343C22×C139semidirect
604. #343C22×C139semidirect
605. #339C22×C139semidirect
606. #339C22×C139semidirect
725. #104D4×C139semidirect
858. M16C2×D4×C139semidirect
898. C42C2×D4×C139semidirect
1036. C22#455×C139semidirect

Maximal subgroups

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

subgroupindex
#3488×C1392
#3056×C1392
C2×#455×C1392
#3007×C1392
C22×#104×C1392
#2850×C1392
#2040×C1392
#2037×C1392
#2007×C1392
#2004×C1392
#1900×C1392
#1896×C1392
#1882×C1392
#1860×C1392
#1792×C1392
#24467139