Finite Group Databasebeta

← C139×#26010 #48020606

Subgroups — C139×#26010 #48020606

Order 35584.

712 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2439×C139C211yesmaximal, characteristic
2#2345×C139C211yesmaximal, characteristic
3#2101×C139C211yesmaximal, characteristic, complemented
4#2088×C139C211yesmaximal, characteristic, complemented
5#2088×C139C211yesmaximal, characteristic, complemented
6#2057×C139C211yesmaximal, characteristic, complemented
7#1987×C139C211yesmaximal, characteristic, complemented
8#1949×C139C211yesmaximal, characteristic, complemented
9#1919×C139C211yesmaximal, characteristic, complemented
10#1918×C139C211yesmaximal, characteristic, complemented
11#1854×C139C211yesmaximal, characteristic
12#1851×C139C211yesmaximal, characteristic
13#1823×C139C211yesmaximal, characteristic
14#1809×C139C211yesmaximal, characteristic
15#1736×C139C211yesmaximal, characteristic
16C22×M16×C139C2211yescharacteristic
17C2×C4⋊Q8×C139C2211yescharacteristic
18C2×#117×C139C2211yescharacteristic
19C22×C4⋊C4×C139C2211yescharacteristic
20C2×#107×C139C2211yescharacteristic
21C2×#107×C139C2211yescharacteristic
22C2×#106×C139C2211yescharacteristic
23C2×#106×C139C2211yescharacteristic
24C2×C4⋊C8×C139C2211yescharacteristic
25C2×C4⋊C8×C139C2211yescharacteristic
26C2×C22⋊C8×C139C2211yescharacteristic
27#396×C139—21no—
28#393×C139—21no—
29#391×C139—21no—
30#389×C139C2211yescharacteristic
31#389×C139C2211yescharacteristic
32#389×C139C2211yescharacteristic
33#389×C139C2211yescharacteristic
34#387×C139—21no—
35#387×C139—21no—
36#387×C139—21no—
37#382×C139C2211yescharacteristic
38#380×C139—21no—
39#380×C139C2211yescharacteristic
40#380×C139C2211yescharacteristic
41C4×C4⋊C4×C139C2211yescharacteristic
42C4×C4⋊C4×C139C2211yescharacteristic
43C4×C22⋊C4×C139—21no—
44C4×C22⋊C4×C139C2211yescharacteristic
45#340×C139C2211yescharacteristic
46#340×C139C2211yescharacteristic
47#340×C139C2211yescharacteristic
48#340×C139C2211yescharacteristic
49#340×C139C2211yescharacteristic
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C22×Q8×C139—21no—
60C23×C4×C139—21no—
61C23×C4×C139C2311yescharacteristic
62C2×M16×C139—22no—
63C2×M16×C139—22no—
64C2×M16×C139—41no—
65C22×C8×C139C2311yescharacteristic
66C22×C8×C139C2311yescharacteristic
67C22×C8×C139C2311yescharacteristic
68C22×C8×C139C2311yescharacteristic
69C4⋊Q8×C139—22no—
70C4⋊Q8×C139—41no—
71#117×C139—22no—
72#117×C139—41no—
73C2×C4⋊C4×C139—21no—
74C2×C4⋊C4×C139—22no—
75C2×C4⋊C4×C139—21no—
76C2×C4⋊C4×C139—21no—
77C2×C4⋊C4×C139—21no—
78C2×C4⋊C4×C139—21no—
79C2×C4⋊C4×C139—21no—
80C2×C4⋊C4×C139Q814yescomplemented
81C2×C4⋊C4×C139C2311yescharacteristic
82C2×C4⋊C4×C139C2311yescharacteristic
83C2×C4⋊C4×C139C2311yescharacteristic
84C2×C4⋊C4×C139C2311yescharacteristic
85C2×C4⋊C4×C139C2311yescharacteristic
86C2×C4⋊C4×C139C2311yescharacteristic
87C2×C4⋊C4×C139C2311yescharacteristic
88C2×C4⋊C4×C139C2311yescharacteristic
89C2×C22⋊C4×C139—21no—
90C2×C22⋊C4×C139—21no—
91C2×C22⋊C4×C139—21no—
92C2×C22⋊C4×C139D411yescharacteristic
93C2×C22⋊C4×C139D411yescharacteristic
94C2×C42×C139—21no—
95C2×C42×C139—21no—
96C2×C42×C139—21no—
97C2×C42×C139C2311yescharacteristic
98C2×C42×C139C2311yescharacteristic
99#107×C139—22no—
100#107×C139—41no—
101#106×C139—22no—
102#106×C139—41no—
103C4⋊C8×C139—22no—
104C4⋊C8×C139—41no—
105C22⋊C8×C139—22no—
106#95×C139—21no—
107#95×C139—21no—
108#95×C139—21no—
109#95×C139—21no—
110#95×C139—21no—
111#95×C139—21no—
112#95×C139—21no—
113#95×C139—21no—
114#95×C139—21no—
115#95×C139—21no—
116#95×C139D411yescharacteristic
117#95×C139D411yescharacteristic
118C24×C139C2×D411yescharacteristic
119C2×Q8×C139—42no—
120C2×Q8×C139—42no—
121C2×Q8×C139—81no—
122C22×C4×C139—21no—
123C22×C4×C139—21no—
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—24no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—21no—
134C22×C4×C139—21no—
135C22×C4×C139—81no—
136C22×C4×C139—81no—
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139C2×D411yescharacteristic
140C22×C4×C139C2×D411yescharacteristic
141C22×C4×C139C2×D411yescharacteristic
142C22×C4×C139C2×Q812yes—
143C22×C4×C139#4112yes—
144C22×C4×C139C2411yescharacteristic
145M16×C139—44no—
146C2×C8×C139—21no—
147C2×C8×C139—21no—
148C2×C8×C139—21no—
149C2×C8×C139—21no—
150C2×C8×C139—21no—
151C2×C8×C139—21no—
152C2×C8×C139—21no—
153C2×C8×C139—21no—
154C2×C8×C139—21no—
155C2×C8×C139—21no—
156C2×C8×C139—21no—
157C2×C8×C139#4112yes—
158C4⋊C4×C139—24no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—21no—
162C4⋊C4×C139—21no—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—21no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—21no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—21no—
171C4⋊C4×C139—21no—
172C4⋊C4×C139—42no—
173C4⋊C4×C139—42no—
174C4⋊C4×C139—81no—
175C4⋊C4×C139—81no—
176C4⋊C4×C139—81no—
177C4⋊C4×C139C2×Q812yes—
178C4⋊C4×C139C2×Q812yes—
179C4⋊C4×C139#4112yes—
180C22⋊C4×C139—22no—
181C22⋊C4×C139—41no—
182C22⋊C4×C139—42no—
183C22⋊C4×C139—42no—
184C22⋊C4×C139—81no—
185C42×C139—21no—
186C42×C139—21no—
187C42×C139—21no—
188C42×C139—21no—
189C42×C139—42no—
190C42×C139—81no—
191C42×C139—81no—
192C23×C139—21no—
193C23×C139—21no—
194C23×C139—21no—
195C23×C139—21no—
196C23×C139—21no—
197C23×C139—21no—
198C23×C139C22⋊Q812yes—
199C23×C139C22×D411yescharacteristic
200Q8×C139—84no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—22no—
206C2×C4×C139—22no—
207C2×C4×C139—22no—
208C2×C4×C139—22no—
209C2×C4×C139—22no—
210C2×C4×C139—22no—
211C2×C4×C139—21no—
212C2×C4×C139—22no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—41no—
222C2×C4×C139—41no—
223C2×C4×C139—41no—
224C2×C4×C139—41no—
225C2×C4×C139—41no—
226C2×C4×C139—41no—
227C2×C4×C139—41no—
228C2×C4×C139—41no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—84no—
243C2×C4×C139C22⋊Q812yes—
244C2×C4×C139#13712yes—
245C2×C4×C139C22×Q811yescharacteristic
246C2×C4×C139C2×#4111yescharacteristic
247C2×C4×C139C2×#4111yescharacteristic
248C2×C4×C139C2×#4111yescharacteristic
249C2×C4×C139H(5,𝔽2)11yescharacteristic
250C2×C4×C1392−1+411yescharacteristic
251C8×C139—22no—
252C8×C139—41no—
253C8×C139—41no—
254C8×C139—41no—
255C22×C139—22no—
256C22×C139—22no—
257C22×C139—22no—
258C22×C139—41no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139C2×C22⋊Q811yescharacteristic
263C22×C139#54611yescharacteristic
264C22×C139#54711yescharacteristic
265C22×C139C2×#13711yescharacteristic
266C22×C139#57511yescharacteristic
267C22×C139#57611yescharacteristic
268C22×C139#57711yescharacteristic
269C4×C139—22no—
270C4×C139—22no—
271C4×C139—42no—
272C4×C139—42no—
273C4×C139—41no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—42no—
277C4×C139—81no—
278C4×C139—81no—
279C4×C139—81no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139#53311yescharacteristic
283C4×C139#54411yescharacteristic
284C4×C139#55111yescharacteristic
285C4×C139#55211yescharacteristic
286C2×C139—42no—
287C2×C139#243811yescharacteristic
288C2×C139#307811yescharacteristic
289C2×C139#308111yescharacteristic
290C2×C139#331611yescharacteristic
291C2×C139#332211yescharacteristic
292C2×C139#335011yescharacteristic
293C2×C139#335711yescharacteristic
294#26010C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#2601011yescharacteristic, direct product factor, Sylow
296#2439C2×C13911yescharacteristic
297#2345C2×C13911yescharacteristic
298#2101C2×C13911yescharacteristic, complemented
299#2088C2×C13911yescharacteristic, complemented
300#2088C2×C13911yescharacteristic, complemented
301#2057C2×C13911yescharacteristic, complemented
302#1987C2×C13911yescharacteristic, complemented
303#1949C2×C13911yescharacteristic, complemented
304#1919C2×C13911yescharacteristic, complemented
305#1918C2×C13911yescharacteristic, complemented
306#1854C2×C13911yescharacteristic
307#1851C2×C13911yescharacteristic
308#1823C2×C13911yescharacteristic
309#1809C2×C13911yescharacteristic
310#1736C2×C13911yescharacteristic
311C22×M16C22×C13911yescharacteristic
312C2×C4⋊Q8C22×C13911yescharacteristic
313C2×#117C22×C13911yescharacteristic
314C22×C4⋊C4C22×C13911yescharacteristic
315C2×#107C22×C13911yescharacteristic
316C2×#107C22×C13911yescharacteristic
317C2×#106C22×C13911yescharacteristic
318C2×#106C22×C13911yescharacteristic
319C2×C4⋊C8C22×C13911yescharacteristic
320C2×C4⋊C8C22×C13911yescharacteristic
321C2×C22⋊C8C22×C13911yescharacteristic
322#396—21no—
323#393—21no—
324#391—21no—
325#389C22×C13911yescharacteristic
326#389C22×C13911yescharacteristic
327#389C22×C13911yescharacteristic
328#389C22×C13911yescharacteristic
329#387—21no—
330#387—21no—
331#387—21no—
332#382C22×C13911yescharacteristic
333#380—21no—
334#380C22×C13911yescharacteristic
335#380C22×C13911yescharacteristic
336C4×C4⋊C4C22×C13911yescharacteristic
337C4×C4⋊C4C22×C13911yescharacteristic
338C4×C22⋊C4—21no—
339C4×C22⋊C4C22×C13911yescharacteristic
340#340C22×C13911yescharacteristic
341#340C22×C13911yescharacteristic
342#340C22×C13911yescharacteristic
343#340C22×C13911yescharacteristic
344#340C22×C13911yescharacteristic
345#340C22×C13911yescharacteristic
346#340C22×C13911yescharacteristic
347#340C22×C13911yescharacteristic
348#340C22×C13911yescharacteristic
349#340C22×C13911yescharacteristic
350#340C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#336C22×C13911yescharacteristic
353#336C22×C13911yescharacteristic
354C22×Q8—21no—
355C23×C4—21no—
356C23×C4C23×C13911yescharacteristic
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—41no—
360C22×C8C23×C13911yescharacteristic
361C22×C8C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363C22×C8C23×C13911yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8—41no—
366#117—22no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4Q8×C13914yescomplemented
376C2×C4⋊C4C23×C13911yescharacteristic
377C2×C4⋊C4C23×C13911yescharacteristic
378C2×C4⋊C4C23×C13911yescharacteristic
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C4⋊C4C23×C13911yescharacteristic
381C2×C4⋊C4C23×C13911yescharacteristic
382C2×C4⋊C4C23×C13911yescharacteristic
383C2×C4⋊C4C23×C13911yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4D4×C13911yescharacteristic
388C2×C22⋊C4D4×C13911yescharacteristic
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C13911yescharacteristic
393C2×C42C23×C13911yescharacteristic
394#107—22no—
395#107—41no—
396#106—22no—
397#106—41no—
398C4⋊C8—22no—
399C4⋊C8—41no—
400C22⋊C8—22no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95D4×C13911yescharacteristic
412#95D4×C13911yescharacteristic
413C24C2×D4×C13911yescharacteristic
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8—81no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4C2×D4×C13911yescharacteristic
433C22×C4C2×D4×C13911yescharacteristic
434C22×C4C2×D4×C13911yescharacteristic
435C22×C4C2×D4×C13911yescharacteristic
436C22×C4C2×D4×C13911yescharacteristic
437C22×C4C2×Q8×C13912yes—
438C22×C4#41×C13912yes—
439C22×C4C24×C13911yescharacteristic
440M16—44no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8#41×C13912yes—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4C2×Q8×C13912yes—
473C4⋊C4C2×Q8×C13912yes—
474C4⋊C4#41×C13912yes—
475C22⋊C4—22no—
476C22⋊C4—41no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—81no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—81no—
486C42—81no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23C22⋊Q8×C13912yes—
494C23C22×D4×C13911yescharacteristic
495Q8—84no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4C22⋊Q8×C13912yes—
539C2×C4#137×C13912yes—
540C2×C4C22×Q8×C13911yescharacteristic
541C2×C4C2×#41×C13911yescharacteristic
542C2×C4C2×#41×C13911yescharacteristic
543C2×C4C2×#41×C13911yescharacteristic
544C2×C4H(5,𝔽2)×C13911yescharacteristic
545C2×C42−1+4×C13911yescharacteristic
546C8—22no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C22⋊Q8×C13911yescharacteristic
558C22#546×C13911yescharacteristic
559C22#547×C13911yescharacteristic
560C22C2×#137×C13911yescharacteristic
561C22#575×C13911yescharacteristic
562C22#576×C13911yescharacteristic
563C22#577×C13911yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C13911yescharacteristic
578C4#544×C13911yescharacteristic
579C4#551×C13911yescharacteristic
580C4#552×C13911yescharacteristic
581C2—42no—
582C2#2438×C13911yescharacteristic
583C2#3078×C13911yescharacteristic
584C2#3081×C13911yescharacteristic
585C2#3316×C13911yescharacteristic
586C2#3322×C13911yescharacteristic
587C2#3350×C13911yescharacteristic
588C2#3357×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2101×C139C2semidirect
4. #2088×C139C2semidirect
5. #2088×C139C2semidirect
6. #2057×C139C2semidirect
7. #1987×C139C2semidirect
8. #1949×C139C2semidirect
9. #1919×C139C2semidirect
10. #1918×C139C2semidirect
80. C2×C4⋊C4×C139Q8semidirect
294. #26010C139direct (N × H)
295. C139#26010direct (N × H)
298. #2101C2×C139semidirect
299. #2088C2×C139semidirect
300. #2088C2×C139semidirect
301. #2057C2×C139semidirect
302. #1987C2×C139semidirect
303. #1949C2×C139semidirect
304. #1919C2×C139semidirect
305. #1918C2×C139semidirect
375. C2×C4⋊C4Q8×C139semidirect

Maximal subgroups

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

subgroupindex
#2439×C1392
#2345×C1392
#2101×C1392
#2088×C1392
#2057×C1392
#1987×C1392
#1949×C1392
#1919×C1392
#1918×C1392
#1854×C1392
#1851×C1392
#1823×C1392
#1809×C1392
#1736×C1392
#26010139