Finite Group Databasebeta

← C139×#34263 #48028859

Subgroups — C139×#34263 #48028859

Order 35584.

2390 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C139C211yesmaximal, characteristic
2#2357×C139C213yesmaximal, complemented
3#2354×C139C213yesmaximal, complemented
4#2351×C139C211yesmaximal, characteristic, complemented
5Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
6#2345×C139C213yesmaximal, complemented
7#2344×C139C213yesmaximal, complemented
8#2341×C139C211yesmaximal, characteristic
9#2341×C139C211yesmaximal, characteristic
10#2319×C139C213yesmaximal, complemented
11#2314×C139C213yesmaximal, complemented
12#2298×C139C213yesmaximal, complemented
13#2293×C139C213yesmaximal, complemented
14#2276×C139C211yesmaximal, characteristic, complemented
15C42×Q8×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17#520×C139C4116yescomplemented
18C2×C4×Q8×C139C2211yescharacteristic
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×D4×C139C2213yes—
25C2×C4×D4×C139C2213yes—
26C2×#117×C139C2216yes—
27C2×#117×C139C2213yes—
28C22×C4⋊C4×C139C2213yes—
29#390×C139C2213yes—
30#390×C139C2213yes—
31#390×C139C2213yes—
32#390×C139C2213yes—
33#389×C139C2213yes—
34#389×C139C2213yes—
35#389×C139C2213yes—
36#389×C139C2213yes—
37#388×C139C2213yes—
38#388×C139C2216yes—
39#388×C139C2213yes—
40#388×C139C2213yes—
41#388×C139C2213yes—
42#388×C139C2216yes—
43#387×C139C2211yescharacteristic
44#387×C139C2213yes—
45#387×C139C2213yes—
46#387×C139C2213yes—
47#387×C139C2216yes—
48#384×C139C2213yes—
49#382×C139C2213yes—
50#381×C139C2216yes—
51#380×C139C2213yes—
52#380×C139C2213yes—
53#380×C139C2216yes—
54C4×C4⋊C4×C139C2213yes—
55C4×C4⋊C4×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×C139C2216yes—
63C4×C22⋊C4×C139C2213yes—
64C4×C22⋊C4×C139C2213yes—
65#376×C139C2213yes—
66C43×C139C2213yes—
67C2×#41×C139—24no—
68C2×#41×C139—24no—
69C2×#41×C139C2×C418yes—
70C22×Q8×C139C2311yescharacteristic
71C22×D4×C139C2313yes—
72C23×C4×C139C2313yes—
73C23×C4×C139C2316yes—
74C4×Q8×C139—24no—
75C4×Q8×C139—24no—
76C4×Q8×C139—24no—
77C4×Q8×C139—24no—
78C4×Q8×C139C2×C418yes—
79C4×Q8×C139C2×C418yes—
80C4×D4×C139C2×C4124yes—
81C4×D4×C139C2×C4124yes—
82#117×C139—412no—
83#117×C139C2×C4124yes—
84C2×C4⋊C4×C139C2×C4124yes—
85C2×C4⋊C4×C139C2313yes—
86C2×C4⋊C4×C139C2313yes—
87C2×C4⋊C4×C139C2313yes—
88C2×C4⋊C4×C139C2313yes—
89C2×C4⋊C4×C139C2313yes—
90C2×C4⋊C4×C139C2311yescharacteristic
91C2×C4⋊C4×C139C2316yes—
92C2×C4⋊C4×C139C2313yes—
93C2×C4⋊C4×C139C2313yes—
94C2×C4⋊C4×C139C2313yes—
95C2×C4⋊C4×C139C2313yes—
96C2×C4⋊C4×C139C2313yes—
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C22⋊C4×C139C2313yes—
99C2×C22⋊C4×C139C2313yes—
100C2×C22⋊C4×C139C2316yes—
101C2×C22⋊C4×C139C2316yes—
102C2×C22⋊C4×C139C2313yes—
103C2×C22⋊C4×C139C2313yes—
104C2×C22⋊C4×C139C2313yes—
105C2×C22⋊C4×C139C2313yes—
106C2×C42×C139C2313yes—
107C2×C42×C139C2313yes—
108C2×C42×C139C2313yes—
109C2×C42×C139C2313yes—
110C2×C42×C139C2313yes—
111C2×C42×C139C2311yescharacteristic
112C2×C42×C139C2316yes—
113C2×C42×C139C2313yes—
114C2×C42×C139C2313yes—
115C2×C42×C139C2313yes—
116C2×C42×C139C2313yes—
117#95×C139C2311yescharacteristic
118#95×C139C2313yes—
119#95×C139C2313yes—
120#95×C139C2313yes—
121#95×C139C2311yescharacteristic
122#95×C139C2311yescharacteristic
123#95×C139C2313yes—
124#95×C139C2313yes—
125#95×C139C2313yes—
126#95×C139C2316yes—
127#95×C139C2316yes—
128#95×C139C2311yescharacteristic
129#95×C139C2313yes—
130#95×C139C2313yes—
131C24×C139C2413yes—
132#41×C139—232no—
133C2×Q8×C139C22×C414yes—
134C2×Q8×C139#4114yes—
135C2×Q8×C139#4114yes—
136C2×D4×C139—26no—
137C2×D4×C139—26no—
138C2×D4×C139C22×C4112yes—
139C22×C4×C139—26no—
140C22×C4×C139—26no—
141C22×C4×C139—46no—
142C22×C4×C139—46no—
143C22×C4×C139C22×C4112yes—
144C22×C4×C139C22×C4124yes—
145C22×C4×C139C2411yescharacteristic
146C22×C4×C139C2411yescharacteristic
147C22×C4×C139C2413yes—
148C22×C4×C139C2413yes—
149C22×C4×C139C2413yes—
150C22×C4×C139C2413yes—
151C22×C4×C139C2411yescharacteristic
152C22×C4×C139C2411yescharacteristic
153C22×C4×C139C2413yes—
154C22×C4×C139C2411yescharacteristic
155C22×C4×C139C2413yes—
156C22×C4×C139C2411yescharacteristic
157C22×C4×C139C2411yescharacteristic
158C22×C4×C139C2413yes—
159C4⋊C4×C139—26no—
160C4⋊C4×C139—26no—
161C4⋊C4×C139—26no—
162C4⋊C4×C139—26no—
163C4⋊C4×C139—26no—
164C4⋊C4×C139—22no—
165C4⋊C4×C139—43no—
166C4⋊C4×C139—43no—
167C4⋊C4×C139—46no—
168C4⋊C4×C139C22×C4112yes—
169C4⋊C4×C139C22×C4112yes—
170C4⋊C4×C139C22×C4112yes—
171C4⋊C4×C139C22×C414yes—
172C22⋊C4×C139—26no—
173C22⋊C4×C139—26no—
174C22⋊C4×C139—46no—
175C22⋊C4×C139—43no—
176C22⋊C4×C139—43no—
177C22⋊C4×C139—46no—
178C22⋊C4×C139C22×C4112yes—
179C22⋊C4×C139C22×C4112yes—
180C42×C139—26no—
181C42×C139—26no—
182C42×C139—26no—
183C42×C139—26no—
184C42×C139—26no—
185C42×C139—22no—
186C42×C139—43no—
187C42×C139—43no—
188C42×C139—46no—
189C42×C139C22×C4112yes—
190C42×C139C22×C4112yes—
191C23×C139—23no—
192C23×C139—23no—
193C23×C139—23no—
194C23×C139—23no—
195C23×C139—23no—
196C23×C139—23no—
197C23×C139C23×C416yes—
198C23×C139C2511yescharacteristic
199Q8×C139#117116yescomplemented
200D4×C139—224no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—23no—
206C2×C4×C139—23no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—21no—
212C2×C4×C139—23no—
213C2×C4×C139—21no—
214C2×C4×C139—23no—
215C2×C4×C139—224no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—23no—
219C2×C4×C139—23no—
220C2×C4×C139—23no—
221C2×C4×C139—23no—
222C2×C4×C139—23no—
223C2×C4×C139—23no—
224C2×C4×C139—23no—
225C2×C4×C139—23no—
226C2×C4×C139—21no—
227C2×C4×C139—23no—
228C2×C4×C139—23no—
229C2×C4×C139—23no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—23no—
233C2×C4×C139—21no—
234C2×C4×C139—424no—
235C2×C4×C139C23×C412yes—
236C2×C4×C139C23×C412yes—
237C2×C4×C139C23×C416yes—
238C2×C4×C139C23×C416yes—
239C2×C4×C139C23×C412yes—
240C2×C4×C139C23×C416yes—
241C2×C4×C139C2×#4116yes—
242C2×C4×C139C2×#4116yes—
243C2×C4×C139H(5,𝔽2)12yes—
244C2×C4×C1392−1+412yes—
245C22×C139—26no—
246C22×C139—26no—
247C22×C139—26no—
248C22×C139—43no—
249C22×C139—43no—
250C22×C139—43no—
251C22×C139—43no—
252C22×C139C24×C411yescharacteristic
253C22×C139C22×#4111yescharacteristic
254C22×C139C22×#4111yescharacteristic
255C22×C139C2×H(5,𝔽2)11yescharacteristic
256C22×C139C2×2−1+411yescharacteristic
257C22×C139#58511yescharacteristic
258C22×C139#58511yescharacteristic
259C4×C139—22no—
260C4×C139—26no—
261C4×C139—26no—
262C4×C139—22no—
263C4×C139—22no—
264C4×C139—22no—
265C4×C139—22no—
266C4×C139—41no—
267C4×C139—43no—
268C4×C139—43no—
269C4×C139—43no—
270C4×C139—41no—
271C4×C139—43no—
272C4×C139C2×#117112yes—
273C2×C139—46no—
274C2×C139C22×#11711yescharacteristic
275C2×C139C4×H(5,𝔽2)11yescharacteristic
276C2×C139C4×2−1+411yescharacteristic
277C2×C139#351611yescharacteristic
278C2×C139#351711yescharacteristic
279C2×C139#352211yescharacteristic
280C2×C139#352411yescharacteristic
281#34263C13911yesmaximal, characteristic, direct product factor, Sylow
282C139#3426311yescharacteristic, direct product factor, Sylow
283C2×#520C2×C13911yescharacteristic
284#2357C2×C13913yescomplemented
285#2354C2×C13913yescomplemented
286#2351C2×C13911yescharacteristic, complemented
287Q8×C4⋊C4C2×C13911yescharacteristic, complemented
288#2345C2×C13913yescomplemented
289#2344C2×C13913yescomplemented
290#2341C2×C13911yescharacteristic
291#2341C2×C13911yescharacteristic
292#2319C2×C13913yescomplemented
293#2314C2×C13913yescomplemented
294#2298C2×C13913yescomplemented
295#2293C2×C13913yescomplemented
296#2276C2×C13911yescharacteristic, complemented
297C42×Q8C2×C13911yescharacteristic, complemented
298C22×#41C22×C13911yescharacteristic
299#520C4×C139116yescomplemented
300C2×C4×Q8C22×C13911yescharacteristic
301C2×C4×Q8C22×C13911yescharacteristic
302C2×C4×Q8C22×C13911yescharacteristic
303C2×C4×Q8C22×C13911yescharacteristic
304C2×C4×Q8C22×C13911yescharacteristic
305C2×C4×Q8C22×C13911yescharacteristic
306C2×C4×D4C22×C13913yes—
307C2×C4×D4C22×C13913yes—
308C2×#117C22×C13916yes—
309C2×#117C22×C13913yes—
310C22×C4⋊C4C22×C13913yes—
311#390C22×C13913yes—
312#390C22×C13913yes—
313#390C22×C13913yes—
314#390C22×C13913yes—
315#389C22×C13913yes—
316#389C22×C13913yes—
317#389C22×C13913yes—
318#389C22×C13913yes—
319#388C22×C13916yes—
320#388C22×C13916yes—
321#388C22×C13913yes—
322#388C22×C13913yes—
323#388C22×C13913yes—
324#388C22×C13913yes—
325#387C22×C13913yes—
326#387C22×C13916yes—
327#387C22×C13913yes—
328#387C22×C13913yes—
329#387C22×C13911yescharacteristic
330#384C22×C13913yes—
331#382C22×C13913yes—
332#381C22×C13916yes—
333#380C22×C13913yes—
334#380C22×C13913yes—
335#380C22×C13916yes—
336C4×C4⋊C4C22×C13913yes—
337C4×C4⋊C4C22×C13913yes—
338C4×C4⋊C4C22×C13913yes—
339C4×C4⋊C4C22×C13913yes—
340C4×C4⋊C4C22×C13913yes—
341C4×C4⋊C4C22×C13913yes—
342C4×C4⋊C4C22×C13913yes—
343C4×C4⋊C4C22×C13913yes—
344C4×C22⋊C4C22×C13913yes—
345C4×C22⋊C4C22×C13913yes—
346C4×C22⋊C4C22×C13916yes—
347#376C22×C13913yes—
348C43C22×C13913yes—
349C2×#41—24no—
350C2×#41—24no—
351C2×#41C2×C4×C13918yes—
352C22×Q8C23×C13911yescharacteristic
353C22×D4C23×C13913yes—
354C23×C4C23×C13913yes—
355C23×C4C23×C13916yes—
356C4×Q8—24no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8C2×C4×C13918yes—
361C4×Q8C2×C4×C13918yes—
362C4×D4C2×C4×C139124yes—
363C4×D4C2×C4×C139124yes—
364#117—412no—
365#117C2×C4×C139124yes—
366C2×C4⋊C4C2×C4×C139124yes—
367C2×C4⋊C4C23×C13913yes—
368C2×C4⋊C4C23×C13913yes—
369C2×C4⋊C4C23×C13913yes—
370C2×C4⋊C4C23×C13913yes—
371C2×C4⋊C4C23×C13913yes—
372C2×C4⋊C4C23×C13911yescharacteristic
373C2×C4⋊C4C23×C13916yes—
374C2×C4⋊C4C23×C13913yes—
375C2×C4⋊C4C23×C13913yes—
376C2×C4⋊C4C23×C13913yes—
377C2×C4⋊C4C23×C13913yes—
378C2×C4⋊C4C23×C13913yes—
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C22⋊C4C23×C13913yes—
381C2×C22⋊C4C23×C13913yes—
382C2×C22⋊C4C23×C13916yes—
383C2×C22⋊C4C23×C13913yes—
384C2×C22⋊C4C23×C13916yes—
385C2×C22⋊C4C23×C13913yes—
386C2×C22⋊C4C23×C13913yes—
387C2×C22⋊C4C23×C13913yes—
388C2×C42C23×C13913yes—
389C2×C42C23×C13913yes—
390C2×C42C23×C13913yes—
391C2×C42C23×C13913yes—
392C2×C42C23×C13913yes—
393C2×C42C23×C13911yescharacteristic
394C2×C42C23×C13916yes—
395C2×C42C23×C13913yes—
396C2×C42C23×C13913yes—
397C2×C42C23×C13913yes—
398C2×C42C23×C13913yes—
399#95C23×C13911yescharacteristic
400#95C23×C13913yes—
401#95C23×C13913yes—
402#95C23×C13913yes—
403#95C23×C13911yescharacteristic
404#95C23×C13911yescharacteristic
405#95C23×C13913yes—
406#95C23×C13913yes—
407#95C23×C13913yes—
408#95C23×C13916yes—
409#95C23×C13916yes—
410#95C23×C13911yescharacteristic
411#95C23×C13913yes—
412#95C23×C13913yes—
413C24C24×C13913yes—
414#41—232no—
415C2×Q8C22×C4×C13914yes—
416C2×Q8#41×C13914yes—
417C2×Q8#41×C13914yes—
418C2×D4—26no—
419C2×D4—26no—
420C2×D4C22×C4×C139112yes—
421C22×C4—26no—
422C22×C4—26no—
423C22×C4—46no—
424C22×C4—46no—
425C22×C4C22×C4×C139112yes—
426C22×C4C22×C4×C139124yes—
427C22×C4C24×C13911yescharacteristic
428C22×C4C24×C13911yescharacteristic
429C22×C4C24×C13913yes—
430C22×C4C24×C13913yes—
431C22×C4C24×C13913yes—
432C22×C4C24×C13913yes—
433C22×C4C24×C13911yescharacteristic
434C22×C4C24×C13911yescharacteristic
435C22×C4C24×C13913yes—
436C22×C4C24×C13911yescharacteristic
437C22×C4C24×C13913yes—
438C22×C4C24×C13911yescharacteristic
439C22×C4C24×C13911yescharacteristic
440C22×C4C24×C13913yes—
441C4⋊C4—26no—
442C4⋊C4—26no—
443C4⋊C4—26no—
444C4⋊C4—26no—
445C4⋊C4—26no—
446C4⋊C4—22no—
447C4⋊C4—43no—
448C4⋊C4—43no—
449C4⋊C4—46no—
450C4⋊C4C22×C4×C139112yes—
451C4⋊C4C22×C4×C139112yes—
452C4⋊C4C22×C4×C139112yes—
453C4⋊C4C22×C4×C13914yes—
454C22⋊C4—26no—
455C22⋊C4—26no—
456C22⋊C4—46no—
457C22⋊C4—43no—
458C22⋊C4—43no—
459C22⋊C4—46no—
460C22⋊C4C22×C4×C139112yes—
461C22⋊C4C22×C4×C139112yes—
462C42—26no—
463C42—26no—
464C42—26no—
465C42—26no—
466C42—26no—
467C42—22no—
468C42—43no—
469C42—43no—
470C42—46no—
471C42C22×C4×C139112yes—
472C42C22×C4×C139112yes—
473C23—23no—
474C23—23no—
475C23—23no—
476C23—23no—
477C23—23no—
478C23—23no—
479C23C23×C4×C13916yes—
480C23C25×C13911yescharacteristic
481Q8#117×C139116yescomplemented
482D4—224no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—23no—
488C2×C4—23no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—23no—
495C2×C4—21no—
496C2×C4—23no—
497C2×C4—224no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—23no—
505C2×C4—23no—
506C2×C4—23no—
507C2×C4—23no—
508C2×C4—21no—
509C2×C4—23no—
510C2×C4—23no—
511C2×C4—23no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—23no—
515C2×C4—21no—
516C2×C4—424no—
517C2×C4C23×C4×C13912yes—
518C2×C4C23×C4×C13912yes—
519C2×C4C23×C4×C13916yes—
520C2×C4C23×C4×C13916yes—
521C2×C4C23×C4×C13912yes—
522C2×C4C23×C4×C13916yes—
523C2×C4C2×#41×C13916yes—
524C2×C4C2×#41×C13916yes—
525C2×C4H(5,𝔽2)×C13912yes—
526C2×C42−1+4×C13912yes—
527C22—26no—
528C22—26no—
529C22—26no—
530C22—43no—
531C22—43no—
532C22—43no—
533C22—43no—
534C22C24×C4×C13911yescharacteristic
535C22C22×#41×C13911yescharacteristic
536C22C22×#41×C13911yescharacteristic
537C22C2×H(5,𝔽2)×C13911yescharacteristic
538C22C2×2−1+4×C13911yescharacteristic
539C22#585×C13911yescharacteristic
540C22#585×C13911yescharacteristic
541C4—22no—
542C4—26no—
543C4—26no—
544C4—22no—
545C4—22no—
546C4—22no—
547C4—22no—
548C4—41no—
549C4—43no—
550C4—43no—
551C4—43no—
552C4—41no—
553C4—43no—
554C4C2×#117×C139112yes—
555C2—46no—
556C2C22×#117×C13911yescharacteristic
557C2C4×H(5,𝔽2)×C13911yescharacteristic
558C2C4×2−1+4×C13911yescharacteristic
559C2#3516×C13911yescharacteristic
560C2#3517×C13911yescharacteristic
561C2#3522×C13911yescharacteristic
562C2#3524×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutatorC22C24×C4×C139
Frattini, cosocleC23C25×C139
prime radicalC22×#41×C139C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2357×C139C2semidirect
3. #2354×C139C2semidirect
4. #2351×C139C2semidirect
5. Q8×C4⋊C4×C139C2semidirect
6. #2345×C139C2semidirect
7. #2344×C139C2semidirect
10. #2319×C139C2semidirect
11. #2314×C139C2semidirect
12. #2298×C139C2semidirect
13. #2293×C139C2semidirect
14. #2276×C139C2semidirect
15. C42×Q8×C139C2semidirect
17. #520×C139C4semidirect
199. Q8×C139#117semidirect
281. #34263C139direct (N × H)
282. C139#34263direct (N × H)
284. #2357C2×C139semidirect
285. #2354C2×C139semidirect
286. #2351C2×C139semidirect
287. Q8×C4⋊C4C2×C139semidirect
288. #2345C2×C139semidirect
289. #2344C2×C139semidirect
292. #2319C2×C139semidirect
293. #2314C2×C139semidirect
294. #2298C2×C139semidirect
295. #2293C2×C139semidirect
296. #2276C2×C139semidirect
297. C42×Q8C2×C139semidirect
299. #520C4×C139semidirect
481. Q8#117×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1392
#2357×C1392
#2354×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2345×C1392
#2344×C1392
#2341×C1392
#2319×C1392
#2314×C1392
#2298×C1392
#2293×C1392
#2276×C1392
C42×Q8×C1392
#34263139