Finite Group Databasebeta

← C139×#36448 #48031044

Subgroups — C139×#36448 #48031044

Order 35584.

1708 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2863×C139C213yesmaximal, complemented
2#2514×C139C213yesmaximal, complemented
3#2514×C139C213yesmaximal, complemented
4#2511×C139C213yesmaximal, complemented
5#2496×C139C213yesmaximal
6#2495×C139C213yesmaximal
7#2494×C139C213yesmaximal
8#2351×C139C211yesmaximal, characteristic, complemented
9#2351×C139C211yesmaximal, characteristic, complemented
10Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
11Q8×C22⋊C4×C139C211yesmaximal, characteristic
12Q8×C22⋊C4×C139C211yesmaximal, characteristic
13Q8×C22⋊C4×C139C211yesmaximal, characteristic
14C4×#126×C139C213yesmaximal
15C42×Q8×C139C211yesmaximal, characteristic, complemented
16C23×Q8×C139C2211yescharacteristic
17C2×#126×C139C2213yes—
18C2×C4×Q8×C139C2211yescharacteristic
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24#401×C139C2216yes—
25#400×C139C2216yes—
26#400×C139C2216yes—
27#397×C139C2216yes—
28#391×C139C2213yes—
29#391×C139C2213yes—
30#391×C139C2213yes—
31#391×C139C2213yes—
32#391×C139C2213yes—
33#391×C139C2213yes—
34#389×C139C2213yes—
35#389×C139C2213yes—
36#389×C139C2213yes—
37#389×C139C2213yes—
38#389×C139C2213yes—
39#389×C139C2213yes—
40#388×C139C2211yescharacteristic
41#388×C139C2213yes—
42#388×C139C2213yes—
43#387×C139C2213yes—
44#387×C139C2216yes—
45#387×C139C2213yes—
46#387×C139C2216yes—
47#387×C139C2213yes—
48#384×C139C2213yes—
49#383×C139C2213yes—
50#383×C139C2216yes—
51#382×C139C2213yes—
52#382×C139C2213yes—
53#380×C139C2213yes—
54#380×C139C2213yes—
55#380×C139C2213yes—
56C4×C4⋊C4×C139C2213yes—
57C4×C4⋊C4×C139C2213yes—
58C4×C4⋊C4×C139C2213yes—
59C4×C4⋊C4×C139C2213yes—
60C4×C4⋊C4×C139C2213yes—
61C4×C4⋊C4×C139C2213yes—
62C4×C22⋊C4×C139C2213yes—
63C4×C22⋊C4×C139C2213yes—
64C4×C22⋊C4×C139C2213yes—
65C43×C139C2213yes—
66C22×Q8×C139—24no—
67C22×Q8×C139—24no—
68C22×Q8×C139—24no—
69C22×Q8×C139C2313yes—
70C22×Q8×C139C2311yescharacteristic
71C23×C4×C139C2313yes—
72#126×C139—212no—
73C4×Q8×C139—24no—
74C4×Q8×C139—24no—
75C4×Q8×C139—24no—
76C4×Q8×C139—24no—
77C4×Q8×C139—24no—
78C4×Q8×C139—24no—
79C2×C4⋊C4×C139C2313yes—
80C2×C4⋊C4×C139C2313yes—
81C2×C4⋊C4×C139C2313yes—
82C2×C4⋊C4×C139C2313yes—
83C2×C4⋊C4×C139C2313yes—
84C2×C4⋊C4×C139C2313yes—
85C2×C4⋊C4×C139C2313yes—
86C2×C4⋊C4×C139C2313yes—
87C2×C4⋊C4×C139C2313yes—
88C2×C4⋊C4×C139C2311yescharacteristic
89C2×C4⋊C4×C139C2313yes—
90C2×C4⋊C4×C139C2316yes—
91C2×C4⋊C4×C139C2313yes—
92C2×C22⋊C4×C139C2313yes—
93C2×C22⋊C4×C139C2313yes—
94C2×C22⋊C4×C139C2311yescharacteristic
95C2×C22⋊C4×C139C2311yescharacteristic
96C2×C22⋊C4×C139C2313yes—
97C2×C22⋊C4×C139C2311yescharacteristic
98C2×C42×C139C2313yes—
99C2×C42×C139C2313yes—
100C2×C42×C139C2313yes—
101C2×C42×C139C2313yes—
102C2×C42×C139C2313yes—
103C2×C42×C139C2313yes—
104C2×C42×C139C2313yes—
105C2×C42×C139C2311yescharacteristic
106C2×C42×C139C2313yes—
107C2×C42×C139C2313yes—
108#95×C139C2316yes—
109#95×C139C2316yes—
110#95×C139C2316yes—
111#95×C139C2313yes—
112#95×C139C2313yes—
113#95×C139C2313yes—
114#95×C139C2316yes—
115#95×C139C2316yes—
116#95×C139C2316yes—
117#95×C139C2313yes—
118#95×C139C2313yes—
119#95×C139C2313yes—
120#95×C139C2313yes—
121#95×C139C2313yes—
122#95×C139C2313yes—
123#95×C139C2311yescharacteristic
124#95×C139C2311yescharacteristic
125#95×C139C2313yes—
126C24×C139C2411yescharacteristic
127C2×Q8×C139—26no—
128C2×Q8×C139—26no—
129C2×Q8×C139—26no—
130C2×Q8×C139—416no—
131C2×Q8×C139#4114yes—
132C2×Q8×C139#4114yes—
133C2×Q8×C139#4114yes—
134C22×C4×C139—26no—
135C22×C4×C139—26no—
136C22×C4×C139—26no—
137C22×C4×C139C2413yes—
138C22×C4×C139C2411yescharacteristic
139C22×C4×C139C2411yescharacteristic
140C22×C4×C139C2413yes—
141C22×C4×C139C2413yes—
142C22×C4×C139C2413yes—
143C22×C4×C139C2413yes—
144C22×C4×C139C2413yes—
145C22×C4×C139C2413yes—
146C22×C4×C139C2411yescharacteristic
147C22×C4×C139C2411yescharacteristic
148C22×C4×C139C2411yescharacteristic
149C22×C4×C139C2411yescharacteristic
150C22×C4×C139C2413yes—
151C4⋊C4×C139—26no—
152C4⋊C4×C139—26no—
153C4⋊C4×C139—26no—
154C4⋊C4×C139—26no—
155C4⋊C4×C139—26no—
156C4⋊C4×C139—26no—
157C4⋊C4×C139—26no—
158C4⋊C4×C139—26no—
159C4⋊C4×C139—26no—
160C4⋊C4×C139—22no—
161C4⋊C4×C139—26no—
162C4⋊C4×C139—43no—
163C4⋊C4×C139—46no—
164C22⋊C4×C139—26no—
165C22⋊C4×C139—26no—
166C22⋊C4×C139—22no—
167C22⋊C4×C139—22no—
168C22⋊C4×C139—43no—
169C22⋊C4×C139#4114yes—
170C42×C139—26no—
171C42×C139—26no—
172C42×C139—26no—
173C42×C139—26no—
174C42×C139—26no—
175C42×C139—26no—
176C42×C139—26no—
177C42×C139—22no—
178C42×C139—26no—
179C42×C139—43no—
180C23×C139—21no—
181C23×C139—21no—
182C23×C139—21no—
183C23×C139—21no—
184C23×C139—21no—
185C23×C139—21no—
186C23×C139C2×#4112yes—
187C23×C139C2511yescharacteristic
188Q8×C139—412no—
189Q8×C139#126116yescomplemented
190C2×C4×C139—21no—
191C2×C4×C139—21no—
192C2×C4×C139—21no—
193C2×C4×C139—21no—
194C2×C4×C139—21no—
195C2×C4×C139—21no—
196C2×C4×C139—21no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—23no—
201C2×C4×C139—23no—
202C2×C4×C139—23no—
203C2×C4×C139—23no—
204C2×C4×C139—23no—
205C2×C4×C139—23no—
206C2×C4×C139—23no—
207C2×C4×C139—23no—
208C2×C4×C139—23no—
209C2×C4×C139—23no—
210C2×C4×C139—23no—
211C2×C4×C139—23no—
212C2×C4×C139—23no—
213C2×C4×C139—23no—
214C2×C4×C139—23no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—23no—
218C2×C4×C139—23no—
219C2×C4×C139—21no—
220C2×C4×C139—23no—
221C2×C4×C139—23no—
222C2×C4×C139—23no—
223C2×C4×C139—23no—
224C2×C4×C139—21no—
225C2×C4×C139—412no—
226C2×C4×C139C2×#4112yes—
227C2×C4×C139C2×#4112yes—
228C2×C4×C139C2×#4116yes—
229C2×C4×C139C2×#4116yes—
230C2×C4×C139C2×#4116yes—
231C2×C4×C1392−1+412yes—
232C2×C4×C1392−1+412yes—
233C22×C139—22no—
234C22×C139—22no—
235C22×C139—22no—
236C22×C139—41no—
237C22×C139—41no—
238C22×C139—41no—
239C22×C139—41no—
240C22×C139C22×#4111yescharacteristic
241C22×C139C22×#4111yescharacteristic
242C22×C139C22×#4111yescharacteristic
243C22×C139C22×#4111yescharacteristic
244C22×C139C2×2−1+411yescharacteristic
245C22×C139C2×2−1+411yescharacteristic
246C22×C139#58511yescharacteristic
247C4×C139—22no—
248C4×C139—22no—
249C4×C139—22no—
250C4×C139—22no—
251C4×C139—43no—
252C4×C139—43no—
253C4×C139—43no—
254C4×C139—43no—
255C4×C139—43no—
256C4×C139—43no—
257C4×C139—41no—
258C4×C139—43no—
259C4×C139—41no—
260C4×C139C2×#126112yes—
261C2×C139—42no—
262C2×C139C22×#12611yescharacteristic
263C2×C139#348011yescharacteristic
264C2×C139#348211yescharacteristic
265C2×C139#348211yescharacteristic
266C2×C139#351611yescharacteristic
267C2×C139#351811yescharacteristic
268C2×C139#352311yescharacteristic
269#36448C13911yesmaximal, characteristic, direct product factor, Sylow
270C139#3644811yescharacteristic, direct product factor, Sylow
271#2863C2×C13913yescomplemented
272#2514C2×C13913yescomplemented
273#2514C2×C13913yescomplemented
274#2511C2×C13913yescomplemented
275#2496C2×C13913yes—
276#2495C2×C13913yes—
277#2494C2×C13913yes—
278#2351C2×C13911yescharacteristic, complemented
279#2351C2×C13911yescharacteristic, complemented
280Q8×C4⋊C4C2×C13911yescharacteristic, complemented
281Q8×C22⋊C4C2×C13911yescharacteristic
282Q8×C22⋊C4C2×C13911yescharacteristic
283Q8×C22⋊C4C2×C13911yescharacteristic
284C4×#126C2×C13913yes—
285C42×Q8C2×C13911yescharacteristic, complemented
286C23×Q8C22×C13911yescharacteristic
287C2×#126C22×C13913yes—
288C2×C4×Q8C22×C13911yescharacteristic
289C2×C4×Q8C22×C13911yescharacteristic
290C2×C4×Q8C22×C13911yescharacteristic
291C2×C4×Q8C22×C13911yescharacteristic
292C2×C4×Q8C22×C13911yescharacteristic
293C2×C4×Q8C22×C13911yescharacteristic
294#401C22×C13916yes—
295#400C22×C13916yes—
296#400C22×C13916yes—
297#397C22×C13916yes—
298#391C22×C13913yes—
299#391C22×C13913yes—
300#391C22×C13913yes—
301#391C22×C13913yes—
302#391C22×C13913yes—
303#391C22×C13913yes—
304#389C22×C13913yes—
305#389C22×C13913yes—
306#389C22×C13913yes—
307#389C22×C13913yes—
308#389C22×C13913yes—
309#389C22×C13913yes—
310#388C22×C13911yescharacteristic
311#388C22×C13913yes—
312#388C22×C13913yes—
313#387C22×C13913yes—
314#387C22×C13913yes—
315#387C22×C13913yes—
316#387C22×C13916yes—
317#387C22×C13916yes—
318#384C22×C13913yes—
319#383C22×C13913yes—
320#383C22×C13916yes—
321#382C22×C13913yes—
322#382C22×C13913yes—
323#380C22×C13913yes—
324#380C22×C13913yes—
325#380C22×C13913yes—
326C4×C4⋊C4C22×C13913yes—
327C4×C4⋊C4C22×C13913yes—
328C4×C4⋊C4C22×C13913yes—
329C4×C4⋊C4C22×C13913yes—
330C4×C4⋊C4C22×C13913yes—
331C4×C4⋊C4C22×C13913yes—
332C4×C22⋊C4C22×C13913yes—
333C4×C22⋊C4C22×C13913yes—
334C4×C22⋊C4C22×C13913yes—
335C43C22×C13913yes—
336C22×Q8—24no—
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8C23×C13913yes—
340C22×Q8C23×C13911yescharacteristic
341C23×C4C23×C13913yes—
342#126—212no—
343C4×Q8—24no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8—24no—
349C2×C4⋊C4C23×C13913yes—
350C2×C4⋊C4C23×C13913yes—
351C2×C4⋊C4C23×C13913yes—
352C2×C4⋊C4C23×C13913yes—
353C2×C4⋊C4C23×C13913yes—
354C2×C4⋊C4C23×C13913yes—
355C2×C4⋊C4C23×C13913yes—
356C2×C4⋊C4C23×C13913yes—
357C2×C4⋊C4C23×C13913yes—
358C2×C4⋊C4C23×C13911yescharacteristic
359C2×C4⋊C4C23×C13913yes—
360C2×C4⋊C4C23×C13913yes—
361C2×C4⋊C4C23×C13916yes—
362C2×C22⋊C4C23×C13913yes—
363C2×C22⋊C4C23×C13913yes—
364C2×C22⋊C4C23×C13911yescharacteristic
365C2×C22⋊C4C23×C13911yescharacteristic
366C2×C22⋊C4C23×C13913yes—
367C2×C22⋊C4C23×C13911yescharacteristic
368C2×C42C23×C13913yes—
369C2×C42C23×C13913yes—
370C2×C42C23×C13913yes—
371C2×C42C23×C13913yes—
372C2×C42C23×C13913yes—
373C2×C42C23×C13913yes—
374C2×C42C23×C13913yes—
375C2×C42C23×C13911yescharacteristic
376C2×C42C23×C13913yes—
377C2×C42C23×C13913yes—
378#95C23×C13913yes—
379#95C23×C13913yes—
380#95C23×C13913yes—
381#95C23×C13913yes—
382#95C23×C13913yes—
383#95C23×C13913yes—
384#95C23×C13911yescharacteristic
385#95C23×C13911yescharacteristic
386#95C23×C13916yes—
387#95C23×C13913yes—
388#95C23×C13913yes—
389#95C23×C13913yes—
390#95C23×C13913yes—
391#95C23×C13916yes—
392#95C23×C13916yes—
393#95C23×C13916yes—
394#95C23×C13916yes—
395#95C23×C13916yes—
396C24C24×C13911yescharacteristic
397C2×Q8—26no—
398C2×Q8—26no—
399C2×Q8—26no—
400C2×Q8—416no—
401C2×Q8#41×C13914yes—
402C2×Q8#41×C13914yes—
403C2×Q8#41×C13914yes—
404C22×C4—26no—
405C22×C4—26no—
406C22×C4—26no—
407C22×C4C24×C13913yes—
408C22×C4C24×C13911yescharacteristic
409C22×C4C24×C13911yescharacteristic
410C22×C4C24×C13913yes—
411C22×C4C24×C13913yes—
412C22×C4C24×C13913yes—
413C22×C4C24×C13913yes—
414C22×C4C24×C13913yes—
415C22×C4C24×C13913yes—
416C22×C4C24×C13911yescharacteristic
417C22×C4C24×C13911yescharacteristic
418C22×C4C24×C13911yescharacteristic
419C22×C4C24×C13911yescharacteristic
420C22×C4C24×C13913yes—
421C4⋊C4—26no—
422C4⋊C4—26no—
423C4⋊C4—26no—
424C4⋊C4—26no—
425C4⋊C4—26no—
426C4⋊C4—26no—
427C4⋊C4—26no—
428C4⋊C4—26no—
429C4⋊C4—26no—
430C4⋊C4—22no—
431C4⋊C4—26no—
432C4⋊C4—43no—
433C4⋊C4—46no—
434C22⋊C4—26no—
435C22⋊C4—26no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—43no—
439C22⋊C4#41×C13914yes—
440C42—26no—
441C42—26no—
442C42—26no—
443C42—26no—
444C42—26no—
445C42—26no—
446C42—26no—
447C42—22no—
448C42—26no—
449C42—43no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23C2×#41×C13912yes—
457C23C25×C13911yescharacteristic
458Q8—412no—
459Q8#126×C139116yescomplemented
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—23no—
477C2×C4—23no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—23no—
481C2×C4—23no—
482C2×C4—23no—
483C2×C4—23no—
484C2×C4—23no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—23no—
488C2×C4—23no—
489C2×C4—21no—
490C2×C4—23no—
491C2×C4—23no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—21no—
495C2×C4—412no—
496C2×C4C2×#41×C13912yes—
497C2×C4C2×#41×C13912yes—
498C2×C4C2×#41×C13916yes—
499C2×C4C2×#41×C13916yes—
500C2×C4C2×#41×C13916yes—
501C2×C42−1+4×C13912yes—
502C2×C42−1+4×C13912yes—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22C22×#41×C13911yescharacteristic
511C22C22×#41×C13911yescharacteristic
512C22C22×#41×C13911yescharacteristic
513C22C22×#41×C13911yescharacteristic
514C22C2×2−1+4×C13911yescharacteristic
515C22C2×2−1+4×C13911yescharacteristic
516C22#585×C13911yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—43no—
522C4—43no—
523C4—43no—
524C4—43no—
525C4—43no—
526C4—43no—
527C4—41no—
528C4—43no—
529C4—41no—
530C4C2×#126×C139112yes—
531C2—42no—
532C2C22×#126×C13911yescharacteristic
533C2#3480×C13911yescharacteristic
534C2#3482×C13911yescharacteristic
535C2#3482×C13911yescharacteristic
536C2#3516×C13911yescharacteristic
537C2#3518×C13911yescharacteristic
538C2#3523×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC24×C139C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2863×C139C2semidirect
2. #2514×C139C2semidirect
3. #2514×C139C2semidirect
4. #2511×C139C2semidirect
8. #2351×C139C2semidirect
9. #2351×C139C2semidirect
10. Q8×C4⋊C4×C139C2semidirect
15. C42×Q8×C139C2semidirect
189. Q8×C139#126semidirect
269. #36448C139direct (N × H)
270. C139#36448direct (N × H)
271. #2863C2×C139semidirect
272. #2514C2×C139semidirect
273. #2514C2×C139semidirect
274. #2511C2×C139semidirect
278. #2351C2×C139semidirect
279. #2351C2×C139semidirect
280. Q8×C4⋊C4C2×C139semidirect
285. C42×Q8C2×C139semidirect
459. Q8#126×C139semidirect

Maximal subgroups

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

subgroupindex
#2863×C1392
#2514×C1392
#2511×C1392
#2496×C1392
#2495×C1392
#2494×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
C4×#126×C1392
C42×Q8×C1392
#36448139