Finite Group Databasebeta

← C139×#35883 #48030479

Subgroups — C139×#35883 #48030479

Order 35584.

1622 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2645×C139C213yesmaximal, complemented
2#2514×C139C213yesmaximal, complemented
3#2514×C139C213yesmaximal, complemented
4#2511×C139C213yesmaximal, complemented
5#2497×C139C213yesmaximal
6#2495×C139C213yesmaximal
7#2494×C139C213yesmaximal
8#2401×C139C213yesmaximal
9#2351×C139C211yesmaximal, characteristic, complemented
10#2351×C139C211yesmaximal, characteristic, complemented
11Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
12Q8×C22⋊C4×C139C211yesmaximal, characteristic
13Q8×C22⋊C4×C139C211yesmaximal, characteristic
14Q8×C22⋊C4×C139C211yesmaximal, characteristic
15#2276×C139C211yesmaximal, characteristic, complemented
16C23×Q8×C139C2211yescharacteristic
17C2×C4×Q8×C139C2211yescharacteristic
18C2×C4×Q8×C139C2211yescharacteristic
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23#401×C139C2213yes—
24#401×C139C2216yes—
25#400×C139C2213yes—
26#400×C139C2216yes—
27#400×C139C2213yes—
28#400×C139C2216yes—
29#400×C139C2213yes—
30#397×C139C2211yescharacteristic
31#397×C139C2213yes—
32#397×C139C2213yes—
33#396×C139C2213yes—
34#391×C139C2213yes—
35#391×C139C2213yes—
36#391×C139C2213yes—
37#391×C139C2213yes—
38#391×C139C2213yes—
39#391×C139C2213yes—
40#389×C139C2213yes—
41#389×C139C2213yes—
42#389×C139C2213yes—
43#389×C139C2213yes—
44#389×C139C2213yes—
45#389×C139C2213yes—
46#388×C139C2216yes—
47#387×C139C2216yes—
48#387×C139C2216yes—
49#384×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—
65#376×C139C2213yes—
66C22×Q8×C139—24no—
67C22×Q8×C139—24no—
68C22×Q8×C139—24no—
69C22×Q8×C139C2313yes—
70C22×Q8×C139C2311yescharacteristic
71C23×C4×C139C2313yes—
72C4×Q8×C139—24no—
73C4×Q8×C139—24no—
74C4×Q8×C139—24no—
75C4×Q8×C139—24no—
76C4×Q8×C139—24no—
77C4×Q8×C139—24no—
78C2×C4⋊C4×C139C2313yes—
79C2×C4⋊C4×C139C2311yescharacteristic
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×C139C2313yes—
89C2×C4⋊C4×C139C2313yes—
90C2×C4⋊C4×C139C2316yes—
91C2×C22⋊C4×C139C2311yescharacteristic
92C2×C22⋊C4×C139C2311yescharacteristic
93C2×C22⋊C4×C139C2311yescharacteristic
94C2×C22⋊C4×C139C2313yes—
95C2×C22⋊C4×C139C2313yes—
96C2×C22⋊C4×C139C2313yes—
97C2×C42×C139C2313yes—
98C2×C42×C139C2313yes—
99C2×C42×C139C2313yes—
100C2×C42×C139C2313yes—
101C2×C42×C139C2313yes—
102C2×C42×C139C2313yes—
103C2×C42×C139C2316yes—
104#95×C139C2313yes—
105#95×C139C2311yescharacteristic
106#95×C139C2313yes—
107#95×C139C2311yescharacteristic
108#95×C139C2313yes—
109#95×C139C2313yes—
110#95×C139C2313yes—
111#95×C139C2311yescharacteristic
112#95×C139C2313yes—
113#95×C139C2313yes—
114#95×C139C2313yes—
115#95×C139C2313yes—
116#95×C139C2313yes—
117#95×C139C2313yes—
118#95×C139C2316yes—
119#95×C139C2313yes—
120#95×C139C2313yes—
121#95×C139C2316yes—
122#95×C139C2316yes—
123#95×C139C2316yes—
124#95×C139C2316yes—
125C24×C139C2411yescharacteristic
126C2×Q8×C139—26no—
127C2×Q8×C139—26no—
128C2×Q8×C139—26no—
129C2×Q8×C139—416no—
130C2×Q8×C139#4114yes—
131C2×Q8×C139#4114yes—
132C2×Q8×C139#4114yes—
133C22×C4×C139—26no—
134C22×C4×C139—26no—
135C22×C4×C139—26no—
136C22×C4×C139C2413yes—
137C22×C4×C139C2411yescharacteristic
138C22×C4×C139C2411yescharacteristic
139C22×C4×C139C2411yescharacteristic
140C22×C4×C139C2411yescharacteristic
141C22×C4×C139C2411yescharacteristic
142C22×C4×C139C2413yes—
143C22×C4×C139C2413yes—
144C22×C4×C139C2413yes—
145C22×C4×C139C2413yes—
146C22×C4×C139C2413yes—
147C22×C4×C139C2413yes—
148C22×C4×C139C2411yescharacteristic
149C22×C4×C139C2413yes—
150C4⋊C4×C139—26no—
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—22no—
158C4⋊C4×C139—43no—
159C4⋊C4×C139—43no—
160C4⋊C4×C139—43no—
161C4⋊C4×C139—43no—
162C4⋊C4×C139—46no—
163C22⋊C4×C139—22no—
164C22⋊C4×C139—22no—
165C22⋊C4×C139—26no—
166C22⋊C4×C139—22no—
167C22⋊C4×C139—43no—
168C22⋊C4×C139—43no—
169C42×C139—26no—
170C42×C139—26no—
171C42×C139—26no—
172C42×C139—26no—
173C42×C139—26no—
174C42×C139—26no—
175C42×C139—46no—
176C23×C139—21no—
177C23×C139—21no—
178C23×C139—21no—
179C23×C139—21no—
180C23×C139—21no—
181C23×C139—21no—
182C23×C1392−1+412yes—
183C23×C139C2511yescharacteristic
184Q8×C139—412no—
185Q8×C139#126116yes—
186C2×C4×C139—21no—
187C2×C4×C139—21no—
188C2×C4×C139—21no—
189C2×C4×C139—21no—
190C2×C4×C139—21no—
191C2×C4×C139—21no—
192C2×C4×C139—21no—
193C2×C4×C139—23no—
194C2×C4×C139—23no—
195C2×C4×C139—23no—
196C2×C4×C139—23no—
197C2×C4×C139—23no—
198C2×C4×C139—23no—
199C2×C4×C139—23no—
200C2×C4×C139—23no—
201C2×C4×C139—23no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—23no—
205C2×C4×C139—23no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—23no—
210C2×C4×C139—23no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—23no—
214C2×C4×C139—23no—
215C2×C4×C139—23no—
216C2×C4×C139—23no—
217C2×C4×C139—23no—
218C2×C4×C139—23no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—23no—
222C2×C4×C139—21no—
223C2×C4×C139—23no—
224C2×C4×C139—412no—
225C2×C4×C139C2×#4116yes—
226C2×C4×C139C2×#4116yes—
227C2×C4×C139C2×#4116yes—
228C2×C4×C1392−1+412yes—
229C22×C139—22no—
230C22×C139—22no—
231C22×C139—22no—
232C22×C139—41no—
233C22×C139—41no—
234C22×C139—41no—
235C22×C139—41no—
236C22×C139C22×#4111yescharacteristic
237C22×C139C22×#4111yescharacteristic
238C22×C139C22×#4111yescharacteristic
239C22×C139C2×2−1+411yescharacteristic
240C22×C139C2×2−1+411yescharacteristic
241C22×C139#58511yescharacteristic
242C22×C139#58511yescharacteristic
243C4×C139—22no—
244C4×C139—43no—
245C4×C139—43no—
246C4×C139—41no—
247C4×C139—41no—
248C4×C139—43no—
249C4×C139—43no—
250C4×C139—41no—
251C4×C139—43no—
252C4×C139—41no—
253C4×C139—41no—
254C4×C139—43no—
255C4×C139—43no—
256C4×C139C2×#126112yes—
257C2×C139—42no—
258C2×C139C22×#12611yescharacteristic
259C2×C139#351611yescharacteristic
260C2×C139#351611yescharacteristic
261C2×C139#351611yescharacteristic
262C2×C139#351811yescharacteristic
263C2×C139#352311yescharacteristic
264C2×C139#352411yescharacteristic
265#35883C13911yesmaximal, characteristic, direct product factor, Sylow
266C139#3588311yescharacteristic, direct product factor, Sylow
267#2645C2×C13913yescomplemented
268#2514C2×C13913yescomplemented
269#2514C2×C13913yescomplemented
270#2511C2×C13913yescomplemented
271#2497C2×C13913yes—
272#2495C2×C13913yes—
273#2494C2×C13913yes—
274#2401C2×C13913yes—
275#2351C2×C13911yescharacteristic, complemented
276#2351C2×C13911yescharacteristic, complemented
277Q8×C4⋊C4C2×C13911yescharacteristic, complemented
278Q8×C22⋊C4C2×C13911yescharacteristic
279Q8×C22⋊C4C2×C13911yescharacteristic
280Q8×C22⋊C4C2×C13911yescharacteristic
281#2276C2×C13911yescharacteristic, complemented
282C23×Q8C22×C13911yescharacteristic
283C2×C4×Q8C22×C13911yescharacteristic
284C2×C4×Q8C22×C13911yescharacteristic
285C2×C4×Q8C22×C13911yescharacteristic
286C2×C4×Q8C22×C13911yescharacteristic
287C2×C4×Q8C22×C13911yescharacteristic
288C2×C4×Q8C22×C13911yescharacteristic
289#401C22×C13916yes—
290#401C22×C13913yes—
291#400C22×C13913yes—
292#400C22×C13916yes—
293#400C22×C13916yes—
294#400C22×C13913yes—
295#400C22×C13913yes—
296#397C22×C13911yescharacteristic
297#397C22×C13913yes—
298#397C22×C13913yes—
299#396C22×C13913yes—
300#391C22×C13913yes—
301#391C22×C13913yes—
302#391C22×C13913yes—
303#391C22×C13913yes—
304#391C22×C13913yes—
305#391C22×C13913yes—
306#389C22×C13913yes—
307#389C22×C13913yes—
308#389C22×C13913yes—
309#389C22×C13913yes—
310#389C22×C13913yes—
311#389C22×C13913yes—
312#388C22×C13916yes—
313#387C22×C13916yes—
314#387C22×C13916yes—
315#384C22×C13913yes—
316#383C22×C13916yes—
317#382C22×C13913yes—
318#382C22×C13913yes—
319#380C22×C13913yes—
320#380C22×C13913yes—
321#380C22×C13913yes—
322C4×C4⋊C4C22×C13913yes—
323C4×C4⋊C4C22×C13913yes—
324C4×C4⋊C4C22×C13913yes—
325C4×C4⋊C4C22×C13913yes—
326C4×C4⋊C4C22×C13913yes—
327C4×C4⋊C4C22×C13913yes—
328C4×C22⋊C4C22×C13913yes—
329C4×C22⋊C4C22×C13913yes—
330C4×C22⋊C4C22×C13913yes—
331#376C22×C13913yes—
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8C23×C13913yes—
336C22×Q8C23×C13911yescharacteristic
337C23×C4C23×C13913yes—
338C4×Q8—24no—
339C4×Q8—24no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—24no—
344C2×C4⋊C4C23×C13913yes—
345C2×C4⋊C4C23×C13913yes—
346C2×C4⋊C4C23×C13913yes—
347C2×C4⋊C4C23×C13913yes—
348C2×C4⋊C4C23×C13913yes—
349C2×C4⋊C4C23×C13913yes—
350C2×C4⋊C4C23×C13911yescharacteristic
351C2×C4⋊C4C23×C13913yes—
352C2×C4⋊C4C23×C13913yes—
353C2×C4⋊C4C23×C13913yes—
354C2×C4⋊C4C23×C13913yes—
355C2×C4⋊C4C23×C13913yes—
356C2×C4⋊C4C23×C13916yes—
357C2×C22⋊C4C23×C13911yescharacteristic
358C2×C22⋊C4C23×C13911yescharacteristic
359C2×C22⋊C4C23×C13911yescharacteristic
360C2×C22⋊C4C23×C13913yes—
361C2×C22⋊C4C23×C13913yes—
362C2×C22⋊C4C23×C13913yes—
363C2×C42C23×C13913yes—
364C2×C42C23×C13913yes—
365C2×C42C23×C13913yes—
366C2×C42C23×C13913yes—
367C2×C42C23×C13913yes—
368C2×C42C23×C13913yes—
369C2×C42C23×C13916yes—
370#95C23×C13911yescharacteristic
371#95C23×C13913yes—
372#95C23×C13913yes—
373#95C23×C13913yes—
374#95C23×C13913yes—
375#95C23×C13913yes—
376#95C23×C13913yes—
377#95C23×C13913yes—
378#95C23×C13913yes—
379#95C23×C13913yes—
380#95C23×C13911yescharacteristic
381#95C23×C13911yescharacteristic
382#95C23×C13913yes—
383#95C23×C13913yes—
384#95C23×C13913yes—
385#95C23×C13913yes—
386#95C23×C13916yes—
387#95C23×C13916yes—
388#95C23×C13916yes—
389#95C23×C13916yes—
390#95C23×C13916yes—
391C24C24×C13911yescharacteristic
392C2×Q8—26no—
393C2×Q8—26no—
394C2×Q8—26no—
395C2×Q8—416no—
396C2×Q8#41×C13914yes—
397C2×Q8#41×C13914yes—
398C2×Q8#41×C13914yes—
399C22×C4—26no—
400C22×C4—26no—
401C22×C4—26no—
402C22×C4C24×C13913yes—
403C22×C4C24×C13911yescharacteristic
404C22×C4C24×C13911yescharacteristic
405C22×C4C24×C13911yescharacteristic
406C22×C4C24×C13911yescharacteristic
407C22×C4C24×C13911yescharacteristic
408C22×C4C24×C13913yes—
409C22×C4C24×C13913yes—
410C22×C4C24×C13913yes—
411C22×C4C24×C13913yes—
412C22×C4C24×C13913yes—
413C22×C4C24×C13913yes—
414C22×C4C24×C13911yescharacteristic
415C22×C4C24×C13913yes—
416C4⋊C4—26no—
417C4⋊C4—26no—
418C4⋊C4—26no—
419C4⋊C4—26no—
420C4⋊C4—26no—
421C4⋊C4—26no—
422C4⋊C4—22no—
423C4⋊C4—26no—
424C4⋊C4—43no—
425C4⋊C4—43no—
426C4⋊C4—43no—
427C4⋊C4—43no—
428C4⋊C4—46no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—26no—
432C22⋊C4—22no—
433C22⋊C4—43no—
434C22⋊C4—43no—
435C42—26no—
436C42—26no—
437C42—26no—
438C42—26no—
439C42—26no—
440C42—26no—
441C42—46no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C232−1+4×C13912yes—
449C23C25×C13911yescharacteristic
450Q8—412no—
451Q8#126×C139116yes—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—23no—
460C2×C4—23no—
461C2×C4—23no—
462C2×C4—23no—
463C2×C4—23no—
464C2×C4—23no—
465C2×C4—23no—
466C2×C4—23no—
467C2×C4—23no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—23no—
476C2×C4—23no—
477C2×C4—21no—
478C2×C4—21no—
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—21no—
489C2×C4—23no—
490C2×C4—412no—
491C2×C4C2×#41×C13916yes—
492C2×C4C2×#41×C13916yes—
493C2×C4C2×#41×C13916yes—
494C2×C42−1+4×C13912yes—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22C22×#41×C13911yescharacteristic
503C22C22×#41×C13911yescharacteristic
504C22C22×#41×C13911yescharacteristic
505C22C2×2−1+4×C13911yescharacteristic
506C22C2×2−1+4×C13911yescharacteristic
507C22#585×C13911yescharacteristic
508C22#585×C13911yescharacteristic
509C4—22no—
510C4—43no—
511C4—43no—
512C4—41no—
513C4—41no—
514C4—43no—
515C4—43no—
516C4—41no—
517C4—43no—
518C4—41no—
519C4—41no—
520C4—43no—
521C4—43no—
522C4C2×#126×C139112yes—
523C2—42no—
524C2C22×#126×C13911yescharacteristic
525C2#3516×C13911yescharacteristic
526C2#3516×C13911yescharacteristic
527C2#3516×C13911yescharacteristic
528C2#3518×C13911yescharacteristic
529C2#3523×C13911yescharacteristic
530C2#3524×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. #2645×C139C2semidirect
2. #2514×C139C2semidirect
3. #2514×C139C2semidirect
4. #2511×C139C2semidirect
9. #2351×C139C2semidirect
10. #2351×C139C2semidirect
11. Q8×C4⋊C4×C139C2semidirect
15. #2276×C139C2semidirect
265. #35883C139direct (N × H)
266. C139#35883direct (N × H)
267. #2645C2×C139semidirect
268. #2514C2×C139semidirect
269. #2514C2×C139semidirect
270. #2511C2×C139semidirect
275. #2351C2×C139semidirect
276. #2351C2×C139semidirect
277. Q8×C4⋊C4C2×C139semidirect
281. #2276C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2645×C1392
#2514×C1392
#2511×C1392
#2497×C1392
#2495×C1392
#2494×C1392
#2401×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
#2276×C1392
#35883139