Finite Group Databasebeta

← C139×#26479 #48021075

Subgroups — C139×#26479 #48021075

Order 35584.

792 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C139C211yesmaximal, characteristic, complemented
2C2×#478×C139C211yesmaximal, characteristic
3#2552×C139C211yesmaximal, characteristic, complemented
4#2367×C139C211yesmaximal, characteristic
5#2066×C139C211yesmaximal, characteristic, complemented
6#2065×C139C211yesmaximal, characteristic
7#2026×C139C211yesmaximal, characteristic, complemented
8#2025×C139C211yesmaximal, characteristic
9#1983×C139C211yesmaximal, characteristic
10#1959×C139C211yesmaximal, characteristic
11#1948×C139C211yesmaximal, characteristic, complemented
12#1940×C139C211yesmaximal, characteristic, complemented
13#1865×C139C211yesmaximal, characteristic, complemented
14#1864×C139C211yesmaximal, characteristic
15#1776×C139C211yesmaximal, characteristic, complemented
16C2×#125×C139C2211yescharacteristic
17C2×#125×C139C2211yescharacteristic
18C2×#124×C139C2211yescharacteristic
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×D4×C139C2211yescharacteristic
21#479×C139—24no—
22#478×C139—24no—
23C2×#107×C139C2211yescharacteristic
24C2×#106×C139C2211yescharacteristic
25C2×#106×C139C2211yescharacteristic
26C2×#106×C139C2211yescharacteristic
27C2×C4⋊C8×C139C2211yescharacteristic
28C2×C4⋊C8×C139C2211yescharacteristic
29C2×C4⋊C8×C139C2211yescharacteristic
30C2×#103×C139C2211yescharacteristic
31C2×#103×C139C2211yescharacteristic
32C2×#103×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#97×C139C2211yescharacteristic
39#398×C139—21no—
40#398×C139—21no—
41#391×C139C2211yescharacteristic
42#390×C139C2211yescharacteristic
43#389×C139—21no—
44#389×C139C2211yescharacteristic
45#389×C139C2211yescharacteristic
46#388×C139—21no—
47#388×C139—21no—
48#385×C139—21no—
49#384×C139—21no—
50#384×C139C2211yescharacteristic
51C4×C4⋊C4×C139C2211yescharacteristic
52C4×C4⋊C4×C139C2211yescharacteristic
53C4×C4⋊C4×C139C2211yescharacteristic
54C4×C22⋊C4×C139—21no—
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×Q8×C139C2311yescharacteristic
62C22×D4×C139C2311yescharacteristic
63C23×C4×C139—21no—
64C22×C8×C139C2311yescharacteristic
65C22×C8×C139C2311yescharacteristic
66C22×C8×C139C2311yescharacteristic
67C22×C8×C139C2311yescharacteristic
68#125×C139—22no—
69#125×C139—22no—
70#125×C139—41no—
71#125×C139—41no—
72#124×C139—22no—
73#124×C139Q814yes—
74C4×Q8×C139—22no—
75C4×Q8×C139—41no—
76C4×D4×C139—22no—
77C4×D4×C139—41no—
78C2×C4⋊C4×C139—21no—
79C2×C4⋊C4×C139—21no—
80C2×C4⋊C4×C139—21no—
81C2×C4⋊C4×C139—21no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139—21no—
84C2×C4⋊C4×C139—21no—
85C2×C4⋊C4×C139—21no—
86C2×C4⋊C4×C139—21no—
87C2×C4⋊C4×C139D411yescharacteristic
88C2×C4⋊C4×C139D411yescharacteristic
89C2×C4⋊C4×C139C2311yescharacteristic
90C2×C4⋊C4×C139C2311yescharacteristic
91C2×C4⋊C4×C139C2311yescharacteristic
92C2×C4⋊C4×C139C2311yescharacteristic
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C4⋊C4×C139C2311yescharacteristic
95C2×C22⋊C4×C139—21no—
96C2×C22⋊C4×C139—21no—
97C2×C22⋊C4×C139—21no—
98C2×C22⋊C4×C139—21no—
99C2×C22⋊C4×C139—21no—
100C2×C42×C139—21no—
101C2×C42×C139—21no—
102C2×C42×C139—21no—
103C2×C42×C139C2311yescharacteristic
104C2×C42×C139C2311yescharacteristic
105C2×C42×C139C2311yescharacteristic
106#107×C139D414yes—
107#106×C139—22no—
108#106×C139—22no—
109#106×C139—22no—
110C4⋊C8×C139—22no—
111C4⋊C8×C139—22no—
112C4⋊C8×C139—22no—
113#103×C139—22no—
114#103×C139—22no—
115#103×C139—22no—
116#103×C139—41no—
117#102×C139—22no—
118#102×C139—22no—
119#102×C139—22no—
120#102×C139—41no—
121#97×C139—22no—
122#95×C139—21no—
123#95×C139—21no—
124#95×C139—21no—
125#95×C139—21no—
126#95×C139—21no—
127#95×C139—21no—
128#95×C139D411yescharacteristic
129#95×C139D411yescharacteristic
130C24×C139—21no—
131C2×Q8×C139—21no—
132C2×Q8×C139—21no—
133C2×Q8×C139—21no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139C2×Q812yes—
137C2×D4×C139—21no—
138C2×D4×C139—21no—
139C2×D4×C139—21no—
140C2×D4×C139—21no—
141C2×D4×C139—21no—
142C2×D4×C139C2×Q812yes—
143C22×C4×C139—21no—
144C22×C4×C139—21no—
145C22×C4×C139—21no—
146C22×C4×C139—21no—
147C22×C4×C139—21no—
148C22×C4×C139—21no—
149C22×C4×C139—21no—
150C22×C4×C139—42no—
151C22×C4×C139—42no—
152C22×C4×C139—81no—
153C22×C4×C139C2×D411yescharacteristic
154C22×C4×C139C2×D411yescharacteristic
155C22×C4×C139C2×D411yescharacteristic
156C22×C4×C139C2×D411yescharacteristic
157C22×C4×C139C2×D411yescharacteristic
158C22×C4×C139C2×D411yescharacteristic
159C22×C4×C139C2411yescharacteristic
160C2×C8×C139—21no—
161C2×C8×C139—21no—
162C2×C8×C139—21no—
163C2×C8×C139—21no—
164C2×C8×C139—21no—
165C2×C8×C139—21no—
166C2×C8×C139—21no—
167C2×C8×C139—21no—
168C2×C8×C139—21no—
169C2×C8×C139—21no—
170C2×C8×C139—21no—
171C2×C8×C139C2×D412yes—
172C4⋊C4×C139—21no—
173C4⋊C4×C139—21no—
174C4⋊C4×C139—21no—
175C4⋊C4×C139—21no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—21no—
178C4⋊C4×C139—21no—
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—41no—
182C4⋊C4×C139—41no—
183C4⋊C4×C139—42no—
184C4⋊C4×C139—42no—
185C4⋊C4×C139—42no—
186C4⋊C4×C139—42no—
187C4⋊C4×C139—42no—
188C4⋊C4×C139—42no—
189C4⋊C4×C139—81no—
190C4⋊C4×C139—81no—
191C4⋊C4×C139—81no—
192C4⋊C4×C139C2×D412yes—
193C4⋊C4×C139C2×D412yes—
194C4⋊C4×C139#4112yes—
195C22⋊C4×C139—24no—
196C22⋊C4×C139—24no—
197C22⋊C4×C139—42no—
198C22⋊C4×C139—42no—
199C22⋊C4×C139—81no—
200C42×C139—21no—
201C42×C139—21no—
202C42×C139—21no—
203C42×C139—21no—
204C42×C139—42no—
205C42×C139—42no—
206C42×C139—81no—
207C42×C139C2×Q812yes—
208C42×C139#4112yes—
209C23×C139—22no—
210C23×C139—41no—
211C23×C139—41no—
212C23×C139—41no—
213C23×C139—41no—
214C23×C139—41no—
215C23×C139—41no—
216C23×C139C22×D411yescharacteristic
217Q8×C139—22no—
218Q8×C139—22no—
219Q8×C139—41no—
220Q8×C139—41no—
221D4×C139—22no—
222D4×C139—22no—
223D4×C139—41no—
224D4×C139—41no—
225C2×C4×C139—21no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—22no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—22no—
235C2×C4×C139—22no—
236C2×C4×C139—22no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—21no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—41no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—84no—
263C2×C4×C139C22⋊Q812yes—
264C2×C4×C139C22⋊Q812yes—
265C2×C4×C139C22×D411yescharacteristic
266C2×C4×C139C22×Q811yescharacteristic
267C2×C4×C139C2×#4111yescharacteristic
268C2×C4×C139C2×#4111yescharacteristic
269C2×C4×C139H(5,𝔽2)11yescharacteristic
270C2×C4×C1392−1+411yescharacteristic
271C8×C139—22no—
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C22×C139—42no—
276C22×C139—42no—
277C22×C139—42no—
278C22×C139—81no—
279C22×C139—81no—
280C22×C139—81no—
281C22×C139—81no—
282C22×C139C2×C22⋊Q811yescharacteristic
283C22×C139D4211yescharacteristic
284C22×C139#54811yescharacteristic
285C22×C139#57511yescharacteristic
286C22×C139#57511yescharacteristic
287C22×C139#57711yescharacteristic
288C22×C139#57711yescharacteristic
289C4×C139—22no—
290C4×C139—22no—
291C4×C139—42no—
292C4×C139—42no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—42no—
296C4×C139—42no—
297C4×C139—41no—
298C4×C139—41no—
299C4×C139—81no—
300C4×C139—81no—
301C4×C139—81no—
302C4×C139#53211yescharacteristic
303C4×C139#54211yescharacteristic
304C4×C139D4×Q811yescharacteristic
305C4×C139#55411yescharacteristic
306C2×C139—82no—
307C2×C139#245211yescharacteristic
308C2×C139#308011yescharacteristic
309C2×C139#308411yescharacteristic
310C2×C139#326711yescharacteristic
311C2×C139#327111yescharacteristic
312C2×C139#337111yescharacteristic
313C2×C139#337611yescharacteristic
314#26479C13911yesmaximal, characteristic, direct product factor, Sylow
315C139#2647911yescharacteristic, direct product factor, Sylow
316C2×#479C2×C13911yescharacteristic, complemented
317C2×#478C2×C13911yescharacteristic
318#2552C2×C13911yescharacteristic, complemented
319#2367C2×C13911yescharacteristic
320#2066C2×C13911yescharacteristic, complemented
321#2065C2×C13911yescharacteristic
322#2026C2×C13911yescharacteristic, complemented
323#2025C2×C13911yescharacteristic
324#1983C2×C13911yescharacteristic
325#1959C2×C13911yescharacteristic
326#1948C2×C13911yescharacteristic, complemented
327#1940C2×C13911yescharacteristic, complemented
328#1865C2×C13911yescharacteristic, complemented
329#1864C2×C13911yescharacteristic
330#1776C2×C13911yescharacteristic, complemented
331C2×#125C22×C13911yescharacteristic
332C2×#125C22×C13911yescharacteristic
333C2×#124C22×C13911yescharacteristic
334C2×C4×Q8C22×C13911yescharacteristic
335C2×C4×D4C22×C13911yescharacteristic
336#479—24no—
337#478—24no—
338C2×#107C22×C13911yescharacteristic
339C2×#106C22×C13911yescharacteristic
340C2×#106C22×C13911yescharacteristic
341C2×#106C22×C13911yescharacteristic
342C2×C4⋊C8C22×C13911yescharacteristic
343C2×C4⋊C8C22×C13911yescharacteristic
344C2×C4⋊C8C22×C13911yescharacteristic
345C2×#103C22×C13911yescharacteristic
346C2×#103C22×C13911yescharacteristic
347C2×#103C22×C13911yescharacteristic
348C2×#103C22×C13911yescharacteristic
349C2×#102C22×C13911yescharacteristic
350C2×#102C22×C13911yescharacteristic
351C2×#102C22×C13911yescharacteristic
352C2×#102C22×C13911yescharacteristic
353C2×#97C22×C13911yescharacteristic
354#398—21no—
355#398—21no—
356#391C22×C13911yescharacteristic
357#390C22×C13911yescharacteristic
358#389—21no—
359#389C22×C13911yescharacteristic
360#389C22×C13911yescharacteristic
361#388—21no—
362#388—21no—
363#385—21no—
364#384—21no—
365#384C22×C13911yescharacteristic
366C4×C4⋊C4C22×C13911yescharacteristic
367C4×C4⋊C4C22×C13911yescharacteristic
368C4×C4⋊C4C22×C13911yescharacteristic
369C4×C22⋊C4—21no—
370#340C22×C13911yescharacteristic
371#340C22×C13911yescharacteristic
372#340C22×C13911yescharacteristic
373#340C22×C13911yescharacteristic
374#336C22×C13911yescharacteristic
375#336C22×C13911yescharacteristic
376C22×Q8C23×C13911yescharacteristic
377C22×D4C23×C13911yescharacteristic
378C23×C4—21no—
379C22×C8C23×C13911yescharacteristic
380C22×C8C23×C13911yescharacteristic
381C22×C8C23×C13911yescharacteristic
382C22×C8C23×C13911yescharacteristic
383#125—22no—
384#125—22no—
385#125—41no—
386#125—41no—
387#124—22no—
388#124Q8×C13914yes—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×D4—22no—
392C4×D4—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4D4×C13911yescharacteristic
403C2×C4⋊C4D4×C13911yescharacteristic
404C2×C4⋊C4C23×C13911yescharacteristic
405C2×C4⋊C4C23×C13911yescharacteristic
406C2×C4⋊C4C23×C13911yescharacteristic
407C2×C4⋊C4C23×C13911yescharacteristic
408C2×C4⋊C4C23×C13911yescharacteristic
409C2×C4⋊C4C23×C13911yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42C23×C13911yescharacteristic
419C2×C42C23×C13911yescharacteristic
420C2×C42C23×C13911yescharacteristic
421#107D4×C13914yes—
422#106—22no—
423#106—22no—
424#106—22no—
425C4⋊C8—22no—
426C4⋊C8—22no—
427C4⋊C8—22no—
428#103—22no—
429#103—22no—
430#103—22no—
431#103—41no—
432#102—22no—
433#102—22no—
434#102—22no—
435#102—41no—
436#97—22no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95D4×C13911yescharacteristic
444#95D4×C13911yescharacteristic
445C24—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×Q8×C13912yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C2×Q8×C13912yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4C2×D4×C13911yescharacteristic
469C22×C4C2×D4×C13911yescharacteristic
470C22×C4C2×D4×C13911yescharacteristic
471C22×C4C2×D4×C13911yescharacteristic
472C22×C4C2×D4×C13911yescharacteristic
473C22×C4C2×D4×C13911yescharacteristic
474C22×C4C24×C13911yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8C2×D4×C13912yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4C2×D4×C13912yes—
508C4⋊C4C2×D4×C13912yes—
509C4⋊C4#41×C13912yes—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—42no—
521C42—81no—
522C42C2×Q8×C13912yes—
523C42#41×C13912yes—
524C23—22no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23C22×D4×C13911yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536D4—22no—
537D4—22no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4C22⋊Q8×C13912yes—
579C2×C4C22⋊Q8×C13912yes—
580C2×C4C22×D4×C13911yescharacteristic
581C2×C4C22×Q8×C13911yescharacteristic
582C2×C4C2×#41×C13911yescharacteristic
583C2×C4C2×#41×C13911yescharacteristic
584C2×C4H(5,𝔽2)×C13911yescharacteristic
585C2×C42−1+4×C13911yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C2×C22⋊Q8×C13911yescharacteristic
598C22D42×C13911yescharacteristic
599C22#548×C13911yescharacteristic
600C22#575×C13911yescharacteristic
601C22#575×C13911yescharacteristic
602C22#577×C13911yescharacteristic
603C22#577×C13911yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—42no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4#532×C13911yescharacteristic
618C4#542×C13911yescharacteristic
619C4D4×Q8×C13911yescharacteristic
620C4#554×C13911yescharacteristic
621C2—82no—
622C2#2452×C13911yescharacteristic
623C2#3080×C13911yescharacteristic
624C2#3084×C13911yescharacteristic
625C2#3267×C13911yescharacteristic
626C2#3271×C13911yescharacteristic
627C2#3371×C13911yescharacteristic
628C2#3376×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#479×C139C2semidirect
3. #2552×C139C2semidirect
5. #2066×C139C2semidirect
7. #2026×C139C2semidirect
11. #1948×C139C2semidirect
12. #1940×C139C2semidirect
13. #1865×C139C2semidirect
15. #1776×C139C2semidirect
314. #26479C139direct (N × H)
315. C139#26479direct (N × H)
316. C2×#479C2×C139semidirect
318. #2552C2×C139semidirect
320. #2066C2×C139semidirect
322. #2026C2×C139semidirect
326. #1948C2×C139semidirect
327. #1940C2×C139semidirect
328. #1865C2×C139semidirect
330. #1776C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#479×C1392
C2×#478×C1392
#2552×C1392
#2367×C1392
#2066×C1392
#2065×C1392
#2026×C1392
#2025×C1392
#1983×C1392
#1959×C1392
#1948×C1392
#1940×C1392
#1865×C1392
#1864×C1392
#1776×C1392
#26479139